Pistol is a "swaggering" officer (or "Ensign") who serves under Falstaff in the king's army. Despite Pistol's military duties in the service of the crown, like the rest of the rowdy Eastcheap crew, he is a significant figure in the play's portrayal of civil disorder.
What, you want evidence? Let's see, Pistol's favorite hobbies include brawling in taverns (with men and women) and talking trash, which famously results in him being thrown out of his favorite bar, the Boar's Head Tavern in Act 2, Scene 4. By the end of the play, Pistol is also implicated in the murder of a man (we're not given much information about this) when two officers arrest Doll Tearsheet and Mistress Quickly in Act 5, Scene 4. So, we might say Pistol is kind of a "pistol" – that is, he's explosive, violent, dangerous, and we never know when he might "go off." He's also kind of fun, in a "gosh he's not a good guy, but happens to be entertaining" kind of way.
The title page of the 1600 Quarto edition of the play (which promises the "the humours of Sir John Falstaff, and the swaggering Pistoll,") suggests that Shakespeare's original audiences loved this outrageous character. What's so funny about a violent guy with a big mouth? Well, part of it has to do with the fact that Pistol tends to misquote lines from famous Elizabethan plays like Christopher Marlowe's Tamburlaine the Great (c. 1588), which was known for it's big, bold language and violence. The fact that Pistol mangles the lines suggests that's he's kind of a poser and not entirely in control of his own outrageous language, which seems to make him all the more dangerous and comical.