Is this an archaic form of "please proceed"? I have never heard in in speech but sometimes it appears in novels. My version of "The Adventures of Sherlock Holmes" is full of it, apparently in place of "please".
The NOAD installed on my Mac Mini reported the following definition for pray.
adverb formal or archaic
used as a preface to polite requests or instructions: pray continue.
• used as a way of adding ironic or sarcastic emphasis to a question: and what, pray, was the purpose of that?
In the first example, you can replace pray with please.
Similar definition is given by the Oxford Living Dictionaries.
pray late 13c., "ask earnestly, beg," also "pray to a god or saint," from O.Fr. preier (c.900), from L. precari "ask earnestly, beg," from *prex (plural preces, gen. precis) "prayer, request, entreaty," from PIE base *prek- "to ask, request, entreat" (cf. Skt. prasna-, Avestan frashna- "question;" O.C.S. prositi, Lith. prasyti "to ask, beg;" O.H.G. frahen, Ger. fragen, O.E. fricgan "to ask" a question). Parenthetical expression I pray you, “please, if you will,” attested from 1510s, contracted to pray 16c.
The word "pray" means to earnestly ask something of someone. Therefore, the phrase "pray proceed" could be interpreted as "Please, I beg of you, proceed".
In modern English, we often think of the term "pray" in a spiritual context, but the meaning is the same: to ask something of someone.
See also the version I like enough to consider using in conversation to stage a come back: Prithee tell. The etymology sheds some light on the sometimes sarcastic nature of pray tell.
formal or archaic
1Used as a preface to polite requests or instructions: ladies and gentlemen, pray be seated
1.1Used as a way of adding ironic or sarcastic emphasis to a question: and what, pray, was the purpose of that?
From online Oxford English dictionary