It's a fascinating title which provokes several questions. Is the whole play a dream? Is any part of it supposed to be read as a dream? Who is doing the dreaming?
Many productions and critics, particularly since Peter Brook's famous 1970 staging of the play, have read the play as a wedding night dream of either Theseus or Hippolyta. In this dream, Theseus 'becomes' Oberon, Hippolyta becomes 'Titania', and the lovers' quarrel is translated into something far more passionate and sexual.
The problem with this interpretation is that, as the eminence grise of Shakespearean criticism, Professor Anne Barton of Cambridge, has pointed out, 'how could Theseus possibly Bottom?' She's right: the mechanicals don't really fit into the Theseus' dream interpretation of the play. How does it work?
You could argue this one lots of ways - remember that one character even argues that what has happened to him is a dream:
I have had a dream, past the wit of man to say what dream it was: man is but an ass, if he go about to expound this dream.
I will get Peter Quince to write a ballad of this dream: it shall be called Bottom's Dream, because it hath no bottom; and I will sing it in the latter end of a play...
It's Bottom. He believes that his rendezvous with Titania is like a dream. And, of course, a play is quite like a dream - not real, imaginary, a 'version' of reality. Bottom wants to put his dream into a play: at Thisbe's death. That would be a dream, within a play, within a play , which itself might be intended to be a dream.
Why else is the play like a dream? Remember that the flower goes onto people's eyes when they are asleep. The lovers at the end think that 'we sleep, we dream', as if they are not sure whether they are awake. It is a constant question - are they awake? Are they dreaming? And remember, it is all meetings "by moonlight".
There's no one answer. It's up to you - and your reading of the play.
Hope it helps!