Discuss the role of Tybalt in Romeo and Juliet.

Tybalt is a hothead that Shakespeare uses as a catalyst to make things move faster.  Given that the entire play takes place in three days, some sort of catalyst was necessary.  Tybalt's character made the perfect vessel.
Tybalt is quick to react and embodies the very essence of machismo espoused by the culture.  The very first scene of the play shows us Tybalt's easily lit furor when he practically begs Benvolio to fight him simply because other Montagues and Capulets are fighting.  Tybalt explains that he hates the word "peace" as he "hate(s) hell, all Montagues, and" Benvolio.  In Act 1, Scene 5, we find Tybalt being immediately offended at the presence of Romeo during a Capulet party.  He leaves to get his sword but is stopped by his uncle.  Tybalt than vows, "I will withdraw, but this intrusion shall, / Now seeming sweet, convert to bitterest gall." This gets the ball moving, and Tybalt then sends a letter that essentially asks for a duel with Romeo.  However, Romeo has fallen in love with Tybalt's cousin. Before actually running into Tybalt, Romeo marries Juliet thus making him Tybalt's relative via marriage.  Romeo then refuses to fight Tybalt, which enflames Tybalt even more. When Mercutio stands in for Romeo, Tybalt slays him (though mainly because of Romeo's interference).  Tybalt is then killed by Romeo in revenge for Mercutio's death, and Romeo is banned from the city by the Prince, physically separating him from Juliet.
Without Tybalt, Romeo and Juliet may well have been able to carry on with their secret marriage until a time came that they could reveal what they had been doing. Tybalt's desire to kill Romeo makes sustaining the marriage an impossibility.