I have seen people using this word to refer to the sound wind makes as it moves through trees. However,
1. No reputable dictionary seems to have acknowledged this term as a valid english word.
2. Even Google Ngram seems to agree on its oddness.
It appears to be an obsolete rare term.
Fom the OED Online:
Whispering; a whispering noise, as of leaves moved by the wind.
1872 M. COLLINS Pr. Clarice II. xix. 218 Psithurism of multitudinous leaves made ghostly music.
1875 Blacksmith & Scholar (1876) II. 12 The wind wooed them with a whispering psithurism.
Psithurism(plural not attested)
(obsolete) The sound of rustling leaves.
Origin - An adaptation of the Ancient Greek ψιθύρισµα (psithurisma) or ψιθυρισµός (psithurismos), from ψιθυρίζω (psithurizō, “I whisper”), from ψίθυρος (psithuros, “whispering”, “slanderous”).
The word psithurism first appears as a match in a Google Books search in 1871. It reappears once in 1872, three times in 1874, and one last time in 1876 before slipping into occultation thereafter for the next century or so. Its next vogue began around 1983, seemingly on the strength of being called out as a quaint and colorful obsolete word. I am not at all sure that it has moved very far from that hothouse flower status into real-world usage in its new heyday.
In any event, the record of its original period of usage is not very lengthy. A year before Mortimer Collins used psithurism in The Princess Clarice: A Story of 1871 (1872)—the first instance cited by the OED, as noted in user 66974's answer—he used it in The Secret of Long Life (1871):
Look from your window some March morning of east wind—Eurus, ab urendo—and you may tell the quarter whence it blows by the tortured movement of the trees. They struggle with their aerial tormentor, and shudder as he smites them. Another day the sweet south is blowing ; do you not see how the larch and lime palpitate with pleasure ? . . . do you not hear the musical psithurism of the feathered foliage?
Two years later, Collins was back at it, in Transmigration, volume 1 (1874):
It was love at first sight with us both. I knew it, the very moment I met her glance in that wainscoted Twickenham parlour. She was mine. She knew it also ; a psithurism seemed to pass through her, as when a full-foliaged tree is caught by the wooing south wind. But we were very quiet and polite that afternoon, and neither Mrs. Lovelace nor Captain Charles for one instant suspected what was very well known to Lucy and me ... though without a word.
And then the reactions begin. From a review of Transmigration in The Pall Mall Budget (February 20, 1874):
We felt inclined to address him ["the very tiresome hero of 'Transmigration,' Mr. Mortimer Collins's latest novel—it has been published by the way, at least six weeks, and so, likely enough, it is no longer his latest—"] in some such words as, according to Dr. Hunter, are addressed to the dead among the hill tribes of India. "You have had your good things on earth, your rumpsteak and oyster-sauce, your Presburg biscuits, your Mocha, your red mullet, your 'unquestionable port.' You can no longer have them now. You have talked your nonsense about psithurism, strident, scientists, cheirognomy, trituration, attenuate electric hand, aureate iota, an the rest ; you can no longer talk them now. You have called a spark a scintilla, and a neighbourhood a vicinage ; you cannot so call them again. We will not come to trouble you. See that you do not come to trouble us."
From a review of Transmigration in The Saturday Review of Politics, Literature, Science, and Art (February 28, 1874):
Mr. Mortimer Collins dedicates his latest novel o a lady of rank, "whom," as he writes "all who desire 'the preservation of our religion and our loyalty to our Queen' must honour for her courage in their defence." To what display of courage he refers we are not told. ... Nevertheless, free as is the Queen's person from any risk of violence, we cannot say quite so much of the Queen's English. On this the most outrageous attacks are constantly made, by writers too, like Mr. Mortimer Collins, who cannot plead as their excuse their entire ignorance of language. Mr. Collins is familiar with Greek, so far at least as to enrich his own tongue with the new words "psithurism" and "cheirognomy," and to variegate his pages with scraps of Greek quotation. He has also, we infer, read a good deal of English, for in a letter which he lately wrote to the Times, in correction of a misquotation of an English poet, he informed the world that "inaccurate quotation is a growing vice." He himself, by the way, is happily freer from this vice than most writers of the day ; for when he wants to quote poetry, as he is a poet as well as a novelist, he generally, if we are not mistaken, quotes himself. It would be just as well then, since religion and loyalty are sufficiently safe from attack, if Mr. Collins would refrain from ostentatiously praising ladies for a courage which there has been little room for displaying, and would himself do a little more for the preservation of our language, which is really in considerable danger.
Then comes the instance from Blacksmith and Scholar (1876/1883)—the OED's second cited quotation—which turns out to be a novel by Mortimer Collins:
Under a vast apple-tree in fullest breadth of blossom, the god-like blacksmith, as Homer would have called him, sat on a rustic seat, while Robert Fitz Roy threw himself lazily on the grass, and stretched his flexor and extensor muscles. Down upon the sturdy dwarf and the lithe young Englishman the sunshine danced and flickered through the leaves: the wind wooed them with a whispering psithurism: a mad bobolink just above shouted more loudly than an English thrush in May. Presently through the orchard alleys came tall blue-eyed yellow-haired Devonshire Kezia, with a silver flagon of cider, the juice of the great tree under which they sat. The blacksmith took a mighty draught (for thirst grows by the forge) and silently handed the flagon to Fitz Roy, who left no supernaculum.
So the footprint of psithurism in nineteenth-century English, according to Google Books search results, consists of four uses of the term by the same prolific author and a couple of derisive allusions to it by hostile critics of the author's work.
And that's it for original instances of psithurism for the next 100-odd years. Then come appreciations such as Paul Dickson, Words: a Connoisseur's Collection of Old and New, Weird and Wonderful, Useful and Outlandish Words (1983) [quoted text not shown in snippet window]:
Psithurism. Whispering sound of wind through leaves.
And David Grambs, The Endangered English Dictionary: Bodacious Words Your Dictionary Forgot (1997):
psithurism (SITH-er-iz-um) a whispering sound, as of wind among leaves [example:] a faint and scary psithurism at the edge of the dark woods
It turns out, however, that Mortimer Collins didn't simply pull psithurism out of his copy of Liddell & Scott. The word, in the slightly Greeker form psithurisma, appeared a number of times in nineteenth-century English writing before Collins dropped the final a from it and began trotting it out in novel after turgid novel.
A Google Books search turns up two matches for psithurisma from 1844. From Catherine Long, Sir Roland Ashton: A Tale of the Times (1844):
She endeavoured to feed her dying brother's mind, with the fancies which filled her own, and would tell him "that the sighing of the summer winds in the high branches of the trees—'The Psithurisma of the dark-blue pine—was the voice of those of other days, calling them to join their happy throng!"
And from Leigh Hunt, "A Jar of Honey from Mount Hybla," in Ainsworth's Magazine (1844):
In the opening of Theocritus' first poem, the time of day is a hot noon, and a shepherd and goatherd appear to have been piping under their respective trees;—we suppose at a reasonable distance. The shepherd goes towards the goatherd, who seems to stop playing; and on approaching him, commences the dialogue by observing, that there is something extremely pleasant in the whisper of the pine under which he is sitting, but not less so was the something he was playing just now on his pipe. He declares that he is the next best player after Pan himself; and that if Pan were to have a ram for his prize, the ewe would of necessity fall to the goatherd.
"Αδυ τι το ψιθυρισμα," &c.
Sweet sings the rustling of your pine to-day / Over the fountain-heads; and no less sweet / Upon the pipes play you
The Greek word for rustling, or rather whispering,—psithurisma,—is much admired. "Whispering" is hardly strong enough, and not so long drawn out. There is the continuous whisper in psithurisma.
Then from John Cooke, The Last of the Foresters, Or, Humors on the Border: A Story of the Old Virginia Frontier (1856/1859):
The girl gazed for some moments at the crimson and yellow trees, on which a murmurous laughter of mocking winds arose, at times, and rustled on, and died away into the psithurisma of Theocritus; and the songs of the oriole and mocking-bird fluttering among the ripe fruit, or waving up into the sky, brought a pleasant smile to her lips.
And from T. B., "Home Correspondence," in The Athenæum: A Journal of Literature, Science, the Fine Arts (August 27, 1859):
This was just such a mountain stream as a Greek would have loved, tumbling and brawling as it does from rock to rock, between high banks and ferns, slopes shadowed by ancient oak and ash trees. We take out our Theocritus, and think how Chapman translated for us a passage or two out of the first Idyll.
Sweet is the music which the whispering pine / Makes to the murmuring fountain.
The Greek word is psithurisma,—a word that admirably expresses the soft sibilant swaying, and, so to speak, the curtseying of the boughs. The Latins have caught a little of it in susurrus, and the Northerns in "sough," though this last has a wailful, melancholic sound.
A few further instances of psithurisma appear in the late 1800s—for example, in William Knox Little, "Sermon 7: The Witness to the Sustaining Principle" (1883) in The Witness of the Passion of Our Most Holy Redeemer (1884):
Like the pines of Ida, it [joy] takes the sunlight bravely, because it has been strengthened by the storm; it turns the troubled tempests of life into stirring music; it compels its lighter cares to sing; from sorrow it brings a happy cadence—sad yet happy—like the ψιθυρισμα (psithurisma), the soft low whisper of Sicilian pines.
And in J. Wood, Voices of the Past: A Sacred Drama: in Three Parts (1894):
Everything was so still that I could hear / The softest psithurisma midst the Pines. / In that tranquillity, and perfect peace, she came; / And held me once more to her heart: / Her clasp faint and undefinable (as it was / Not palpable to the touch as the sight) / Thrilled me with a tremulous awe.
It seems, however, that in English psithurisma never escaped Theocritus and the music of the pine tree to become a generalized term for the sound of wind in the leaves of a generic tree (whereas, in contrast, Collins had psithurism operating at full volume through the leaves of an apple tree).
On first acquaintance, it seems hard to take seriously the notion that psithurism was ever a grand old word in English, given that the precise word in question owes its existence entirely to the repeated efforts of a rather poor novelist with an overblown vocabulary to establish it, by adverting to the term on the least provocation in four different novels. But this underrates the extent to which a certain stratum of readers may well have been familiar with the source word ψιθυρισμα through reading the Idylls of Theocritus—or reading other authors (such as Leigh Hunt) who had read them.
Objectively, I think that psithurisma has a stronger claim to English wordhood than Mortimer Collins's shortened form psithurism. Certainly psithurisma was used by more authors with more precision and greater awareness of its pedigree than psithurism was. But perhaps because most of the writers who used it characterized psithurisma as Greek or linked it specifically to the pines of Sicily and to Theocritus, the OED seems to have been more inclined to view it as a foreign word, whereas Collins's baby, being more distinctly his own offspring and subject to his whims, passed muster as English, despite quickly becoming an orphan.