A sexist is someone 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 couldn't vote, wear pants, or own property, you could say that the world was pretty sexist. Likewise, before all-women Vassar College began admitting men, it was accused of having sexist policies. Treating a man or woman differently just because they're male or female is sexist.