Mercutio's language from the beginning of his interaction with Tybalt is belligerent. When Tybalt asks for "a word" with them, Mercutio's aggressive rejoinder is, "but one word with one of us? Couple it with something; make it a word and a blow." That is, he means: "you only want a word? Why don't you make something of it and hit one of us while you're at it."
Tybalt at first refuses to be goaded; he says he will happily strike at them if they give him occasion, to which Mercutio asks, "could you not take some occasion without giving?" That is: "are you not able to take the initiative and start the fight without us offering the opportunity to you directly?"
Tybalt, however, is not really interested in a quarrel with Mercutio; Romeo is his true target. Romeo, meanwhile, tries his best to calm Tybalt's passions, stating, "I . . . love thee better than thou canst devise / Till thou shalt know the reason of my love." He is saying that he understands that Tybalt won't appreciate why Romeo doesn't want to fight with him and would rather be his friend. In the next line, he gives some indication as to why this is, mentioning the name of Capulet. The audience is aware of the reason Romeo has begun to cultivate a fondness for the Capulets, but Tybalt does not yet understand this.