Queen Mab is a fairy queen that is referred to in English fairy mythology along with King Oberon and Queen Titania. She is said to control the fairies, or spirits of the night who can only look at the moon (Stafford, "The Fairy Mythology of England).
In a lengthy speech in Act 1, Scene 4, Mercutio describes Queen Mab as controlling people's dreams. When she passes through "lovers' brains" they dream about being in love; when she passes over courtiers, they dream of bowing before the king at court(I.iv.77). Mercutio even declares that she punishes dreamers for their dreams, as we see him state in the lines, "O'er ladies' lips, who straight on kisses dream, / Which oft the angry Mab with blisters plagues" (79-80). In other words, if Queen Mab passes over a maiden's lips who begins dreaming of kissing a man, Queen Mab then blister's the maiden's lips as punishment for being so loose, even in her dreams.
Mercutio even describes Queen Mab as giving soldiers dreams about killing their enemies (87-88). Finally, he also describes a "parson's" dream, or a member of the clergy's dream, as being about no longer being a member of the clergy, as we see in his lines, "Tickling a parson's nose while as a' lies asleep, / Then dreams he of another benefice" (85-86).
Hence, as we can see, Queen Mab is a fairy queen that Mercutio refers to and describes her as controlling people's dreams while they sleep.