Using pray instead of please in a sentence - Why? When? [closed]

It is somewhat archaic. Today, certain archaic words are often used satirically, when someone is deliberately being too formal or polite (e.g., "Pray tell me, what can I do for you?" when someone is being a nuisance). Words like alas and daresay are examples of the same thing--they're usually used when the speaker wants to be satirical or overly dramatic.

Of course, they are sometimes used genuinely, especially in fiction when a writer wants to give the characters an old-fashioned or classical manner of speaking. If you hear this in the Humanities department from, say, English professors, it's quite possible that they're simply imitating the type of speech they appreciate in older works.