Samson bites his thumb at the Montague's servants because in that time it was a gesture of insult. Rather like "flipping a bird" is in our society or other hand gestures in other cultures are used to indicate insult, anger, and perhaps an invitation to violence.
Samson and Capulet servants like him would have taken on their master's feuds as if they were their own. So, the feud would be fought from the highest head of the family to the lowest servant of one family against the same for the other family in question.
Check out the links below to help you understand gestures and their meanings in different cultures and time periods.
When he bites his thumb is it a great insult and can be the equal to someone flipping someone off nowadays. He was sending an insult to the family.
He was biting his thumb as a strong insult towards the two Montague servants. It used to be considered a rude insult to the British and in Sicily it was a way to say," the hell with you." It is equivalent to flipping someone off with your middle finger nowadays. Samson was sending an insult to the enemy family.
He was biting his thumb at them similar to pointing your middle finger.
Basically biting your thumb during Shakespeare's time is just like pointing your middle finger today .
in shakespear's time biting your thumb was like lifting your middle finger at someone, its an insult, basically
hope it helps