"Nay, as they dare. I will bite my thumb at them, which is a disgrace to them, if they bear it."
Sampson and Gregory are discussing how much they despise the Montague's. They are trying to prove to one another that they are not weak by starting a fight with them. They are trying to get the Montague's to react first and start the fight.
" I will frown as I pass by, and let them take it as they list."
"No, sir. I do not bite my thumb at you, sir, but I bite my thumb, sir."
"Do you bite your thumb at us, sir?"
Sampson decides to bite his thumb at them because it is considered an insult. He is trying to bait them to start the fight by not denying that he is insulting him. Abram sees this and does not like that he is being insulted.
Everyone eventually leaves and Lady Montague is worried about Benvolio's cousin Romeo. She asks Benvolio if he has seen him, Benvolio does not know until Romeo appears and tells him he is upset over a girl.