Romeo is impetuous, changeable, desire. He has some restraint, and some judgment—he doesn't start a fight in the Capulet party, or let himself get drawn into one—but mostly he's girl-crazy, and he finds his last love in Juliet.
Juliet wants to be a good and dutiful daughter—she tries to find ways to make the planned marriage to Paris work for her—but her ability to cut to the heart of things and see the potential for love in Romeo are what govern her.
Tybalt is fiery. He is anger and violence in action.
Mercutio is good with words. He likes to make jokes, and to smooth things over with words when he can. He has a naughty side.
For more on these characters, and the others, see that section of the enotes study guide on the play.
As far as why, they have these characteristics to set the play in motion, to make sure dramatic results happen, and to add tension.