It is a poetic way of replacing the word work in a gender-specific way. To wit:
When the quotation says that Adam delved, it is saying that he delved into the soil of the earth he farmed; this illuminates the connection with the primary meaning of delve. In other words, it is another way to say that he tilled the soil, an old male-specific metaphor for general work in English.
When it says that Eve span, it is similarly referring to a female-specific metaphor for work; not so long ago, women were largely responsible for tailoring and mending the clothing of their household, and even today hobbies like crocheting and knitting are strongly associated with the feminine sex. Weaving cloth in those days would have required a distaff and a spindle; a spindle is a weighted object that spins as it releases cloth to the loom, which explains the use of the participle span.
Though you didn't ask about it in your question, gentlemen had less of a vague meaning than today, where it can be applied to just about anybody, rich or poor; back then, in John Ball's time, to have been called a gentleman would have been to be a man of means, of good family and distinction, and it would connote more of a class divide than we observe with the word today. Indeed, gentlemen has a shared etymological root with the word gentry, which as you'll note still retains that distinction for scholarly use.
So in other words, the quotation can be crudely paraphrased thus:
Back when our righteous forefathers worked, who among them would have been better than the other, who would have observed any class distinctions?
That message would have soundly resonated with the rebels of the Peasant Revolt John Ball was preaching to.
17 And unto Adam he said, Because thou hast hearkened unto the voice of thy wife, and hast eaten of the tree, of which I commanded thee, saying, Thou shalt not eat of it: cursed is the ground for thy sake; in sorrow shalt thou eat of it all the days of thy life;
18 Thorns also and thistles shall it bring forth to thee; and thou shalt eat the herb of the field;
19 In the sweat of thy face shalt thou eat bread, till thou return unto the ground; for out of it wast thou taken: for dust thou art, and unto dust shalt thou return.
20 And Adam called his wife's name Eve; because she was the mother of all living.
21 Unto Adam also and to his wife did the LORD God make coats of skins, and clothed them.