Envy is the sin of wanting (or coveting) what other people have. This can include possessions, power, social standing, or even things that the envious person could not possibly gain for himself, such as talent or looks. It is forbidden by one of the Ten Commandments and also considered one of the Seven Deadly Sins.
The sin of envy is interesting in that it does not cause any direct harm to others by itself. Rather, people commit other sins such as theft or deceit when they act on their envious feelings. (Like other sins, of course, it distances the sinner from God.)