In "A Midsummer Night's Dream" what is accomplished by having the Prologue tell the entire story that the group of men then enact?
Yes, it's an interesting question, and one to which we don't really have a solid answer. It seems to have been a part of Elizabethan and Jacobean stagecraft that, before the play itself, the story of the play was explicitly told in some sort of Prologue.
You see it, for example, in "Romeo and Juliet", where the Prologue tells us right from the start that the play is going to end in the deaths of Romeo and Juliet. You see it in "The Mousetrap", the under-appreciated play-within-a-play in "Hamlet", where a dumb-show actually acts out the plot before it's played out again in the action. So it's not a one-off when it appears in "Pyramus and Thisbe".
However, we're not quite sure why this happened. Some scholars have argued that it's because the Elizabethan audience would wander in and out of the theatre, and so it was important to tell the backbone of the story right at the very start, in order that people could miss a bit and still come back and understand what was going on.
Other scholars have argued - and I think this is quite persuasive - that the Elizabethans didn't enjoy finding out a new story, but enjoyed hearing an old story re-told (remember, nearly all of Shakespeare's plays are re-hashings of existing plots). So you started with the story itself, and then took pleasure in the way the writer was re-telling it, how cleverly it was written and so on.
But the real answer...we just don't know for certain.