eNotes' eText of the play does a great job paraphrasing these lines for you.
Enter Sampson and Gregory with swords and bucklers of the house of Capulet.
SAMP: Gregory, on my word, we'll not carry coals.
SAMP: Gregory, on my word, we will not be humiliated, like carrying coal. GREG: No, for then we should be colliers.
GREG: No, for that we should be coal miners. SAMP: I mean, an we be in choler, we'll draw.
SAMP: I mean, if we are angry, we will draw our swords. GREG: Ay, while you live, draw your neck out of the collar.
GREG: Yeah, while you’re alive, you’ll only draw your neck out of the hangman’s collar.
A pun is a joke that intentionally misuses two or more words that sound alike but mean different things.
In this case, the words are 'colliers' (coal-miners), 'choler' (angry mood), and 'collar' (around your neck, like a noose in this case).
The puns only make sense if you understand some old-fashioned slang. In Shakespeare's time, to 'carry coals' meant to be humiliated. That's where the conversation starts. 'Choler' is like fever (ever heard of cholera, the disease?), and a fever can be kind of like anger (or vice versa). And of course, nobody wants a hangman's collar around their neck.