The "Queen Mab" speech is essentially Mercutio teasing Romeo for pining over Rosaline (whom he loves, but who will not give him the time of day) and trying to amuse him. This "Queen Mab" is the midwife--a woman who helps women give birth--of the fairies, and he carefully describes her as impossibly tiny and delicate. She is "no bigger than an agate-stone / On the fore-finger of an alderman," meaning that she's as small as the stone in a man's ring. Her chariots is an "empty hazelnut"--a hazelnut is about the size of a marble--and it is drawn by "atomies," or creatures as small as atoms. The chariot's wagon spokes are made of the slender legs of spiders, its cover the "wings of grasshoppers." The harness ("traces") is made of spider's web and the collars on the tiny creatures are mere moonbeams. Her chariot driver is a tiny gnat.
Thus, she goes about in the night and makes people dream of whatever they cherish most.