Benvolio and Mercutio talk about this matter at the beginning of act 2, scene 4. The two have unsuccessfully been looking for Romeo, and they express their concern that he has not been seen and that his infatuation with Rosaline will drive him mad. During the two men's discussion, Benvolio informs Mercutio:
Tybalt, the kinsman of old Capulet,
Hath sent a letter to his father's house.
Mercutio assumes that the letter is a summons by Tybalt in which he dares Romeo to duel him. He states:
A challenge, on my life.
It is this scripted challenge which awaits Romeo at his home. Mercutio expresses concern for Romeo by mentioning that his friend now has to contend not only with Rosaline but also with Tybalt's threat. He doubts that Romeo is "man enough" to face Tybalt. He then expresses admiration for Tybalt's dueling skills and, at the same time, mentions what he despises about him and his gang.
Tybalt's challenge stems from his bitter resentment and disgust that Romeo has dared to gatecrash the Capulet ball. In act 1, scene 5, he insists on confronting Romeo during the celebration but is severely scolded by his uncle, Lord Capulet. This stern admonition heightens Tybalt's fury, and he reacts by saying:
I will withdraw: but this intrusion shall
Now seeming sweet convert to bitter gall.
Tybalt's lust for revenge finds expression in the written challenge he sends to the Montague household. The challenge goes unanswered, but Tybalt does later, in act 3, scene 1, confront Romeo. Despite the young Montague's words of appeasement, Tybalt states:
Boy, this shall not excuse the injuries
That thou hast done me; therefore turn and draw.
Tybalt's aggression and Romeo's refusal to be drawn into a fight culminate in a tragedy which forever changes the destinies of not only the two adversaries but of many others too.