The language in the opening dialogue between Sampson and Gregory, Capulet's servants, can be very challenging to follow due to all of the puns and even sexual innuendos found in the lines. Essentially, they are boys being boys and trying to sound boastful about what they will do should they run into any Montagues while walking down the street.
It appears that Sampson is recognized by his friends as typically being the more cowardly one. This is one reason why Sampson opens up the dialogue by declaring he swears they will not be humiliated, which is how we can interpret the line, "Gregory, on my word, we'll not carry coals" (I.i.1). Carrying coals was the lowliest housework assigned to the lowliest servants; therefore, any servant who was assigned to carry coals was frequently insulted and humiliated by the other servants (eNotes). Hence, we know that Sampson is declaring to Gregory that they will not be humiliated. We can surmise that Sampson is proclaiming they will not be humiliated by Sampson's swordsmen abilities. In his next line, Sampson declares, "I mean, an we be in choler, we'll draw," meaning that if they are made angry, they will draw their swords (3). We finally see for certain that it is the Montagues Sampson is speaking of being angered by and fighting against when he further exclaims, "A dog of the house of Montague moves me" (7).
We further see that the real reason why Sampson began the conversation is so that he can defend his bravery and sword fighting abilities. This becomes apparent when Gregory insults Sampson's abilities, saying that he is not "quickly moved to strike [his sword]" and further saying that Sampson is only moved to run away (6, 9-10).
Their conversation continues to include some sexual innuendos. For example, Sampson asserts that he will "push Montague's men from the wall and thrust his maids to the wall" (15-16). However, the essential purpose of the whole dialogue between Sampson and Gregory is to portray the servants as being ridiculous, being boys, and talking about fighting against the Montagues.