Where does Queen Mab travel and how in Romeo and Juliet?

Queen Mab travels through lovers’ brains while they sleep in her special carriage.

Mercutio describes the fairy queen, Queen Mab, in a fanciful monologue.  In Mercutio’s version, Mab travels through the brains of lovers while they sleep at night.  He describes her as “the fairies midwife.”  She has a very interesting and tiny carriage.  

[She] comesIn shape no bigger than an agate-stoneOn the fore-finger of an alderman,Drawn with a team of little...

Queen Mab travels through lovers’ brains while they sleep in her special carriage.

Mercutio describes the fairy queen, Queen Mab, in a fanciful monologue.  In Mercutio’s version, Mab travels through the brains of lovers while they sleep at night.  He describes her as “the fairies midwife.”  She has a very interesting and tiny carriage.  

[She] comes
In shape no bigger than an agate-stone
On the fore-finger of an alderman,
Drawn with a team of little atomies
Athwart men's noses as they lie asleep;
Her wagon-spokes made of long spiders' legs,
The cover of the wings of grasshoppers,
The traces of the smallest spider's web,
The collars of the moonshine's watery beams (Act 1, Scene 4) 

In Mercutio’s mind, Queen Mab’s carriage is an empty hazel-nut.  She makes people dream of love as she visits them.  Each person Queen Mab visits dreams of what matters most to him or her. 

O'er courtiers' knees, that dream on court'sies straight,
O'er lawyers' fingers, who straight dream on fees,
O'er ladies ' lips, who straight on kisses dream,
Which oft the angry Mab with blisters plagues,
Because their breaths with sweetmeats tainted are … (Act 1, Scene 4)

Mercutio is saying this to distract Romeo from his lovesick mourning over Rosaline.  Romeo asks Mercutio to stop being so silly.  Mercutio and Benvolio want Romeo to go to the Capulet ball to take Romeo’s mind off of Rolsaline.  It works better than Romeo expected.  He does forget Rosaline, falling head over heels in love with Juliet.

As silly as this speech is, it is important character development for the quick-witted and silver-tongued Mercutio.  He loves puns and jokes, the dirtier the better, and he is a good friend to Romeo.  Romeo was moody and did not find life worth living, and Mercutio helped cheer him up.  Eventually, Mercutio would give his life defending Romeo.