A malcontent is someone who's always dissatisfied. The guy at the restaurant who sends back the steak because it's too rare, then sends it back a second time complaining that it's not rare enough — he's a malcontent.
Malcontent is often used to describe people who complain about more important things than steaks — things like social and political injustice. In Shakespeare's day, the Malcontent was a popular character type. Hamlet was a classic Malcontent. He believed that his uncle, King Claudius, murdered his father for power, and it made him angry that everyone else seemed to think that Claudius was a good person.