A thug is a bad guy or a bully, especially a violent one. A thug might break into someone's house, push its owners around, and steal their TV.
It's hard to reason with thugs, since they'd rather intimidate and physically hurt people than talk. A playground bully is one kind of thug, and an armed robber is an even more dangerous one. The noun thug may have its oldest roots in the Sanskrit word sthaga-s, "cunning or fraudulent," and it's definitely related to the Marathi and Hindi thag, "cheat or swindler." The earliest use of thug, from 1810, was "member of a murdering gang of robbers in India."