A sexist is someone (usually a man) who discriminates on the basis of gender. Sexist people and laws are unfair.
Like racist and homophobic, this word refers to a type of hatred or discrimination: in this case, on the basis of gender. Usually, sexist people and laws discriminate against women. Back when women weren't allowed to vote, wear pants, or own property, you could say that the world was pretty sexist. Women are still not paid as much as men, which is a sexist situation. But treating a man or woman differently just because they're male or female is sexist.