Shakespeare is a master of wordplay, and one of his specialties is puns, which apply multiple meanings of a word in creative and humorous ways. He incorporates several puns into A Midsummer Night's Dream, and one of the most obvious is Bottom's name. Bottom is a weaver, and his name is associated with his profession, but it can also refer to a person's rear end. Since another slang term for that part of one's anatomy is “ass,” we can easily see where Shakespeare is going with this. Bottom literally turns into an ass (a donkey) during the play—or at least, his head becomes a donkey's head. What's more, Bottom is more than a little bit foolish, so the term “ass” applies well to him in that sense, too.
Bottom himself plays on the word “ass” in act 3, scene 1, when he says, “I see their knavery: this is to make an ass of me; / to fright me, if they could.” Well, someone is certainly going to make an “ass” out of Bottom (or at least out of his head) before the play is over, and he is also made to look extremely ridiculous more than once. The word works on two levels, and the prediction comes true in two very different, and very comical, ways.
Later in the play, other characters also have some fun with a variation on this pun. Bottom is playing the role of Pyramus in the mechanicals' play within a play, and he recites the line “Now die, die, die, die, die” as he pretends to stab himself. Demetrius, apparently feeling somewhat snide, remarks, “No die, but an ace, for him; for he is but one.” How right he is! Demetrius is playing off the word “die,” which can refer to a single dice, but he is also making another pun with the word “ass,” for “ace” was pronounced like “ass” in Shakespeare's day. Bottom, Demetrius implies, is both an original (there is only one of him!) and a fool, but little did he know that the weaver was even a donkey at one point.