Explain the pun words "choler" and "collar."

A pun is a comedic device that capitalizes on the different possible meanings of a word or on two words that sound alike but have altogether different meanings (which is the case in the example about which you ask). Just to give you an example with words that will be more familiar: The Pillsbury Doughboy's speech was wonderful; once he started telling jokes, he was on a roll. The pun here is on the word "roll": to say that someone is on a roll means that they were enjoying a lot of success. However, Pillsbury makes bread rolls, and so the pun capitalizes on both meanings in order to be funny.
At the beginning of act 1, scene 1, Sampson and Gregory enter, presumably talking about their feud with the Montagues. Sampson says, "I mean, an we be in choler, we'll draw," meaning that "If they make us angry, we'll draw our swords to fight them." Choler basically means anger.  Then, Gregory says, "Ay, while you live, draw your neck out of collar," meaning "Yeah, perhaps you should care more about keeping yourself out of trouble [as opposed to be so quick to draw your sword]." Collar is being used as a metaphor for trouble. It is a clever retort to Sampson's bravado, especially because choler and collar sound exactly alike.