Sexism means discrimination against people because of their sex: anything unfair to males or females, because they're males or females, is an example of sexism.
Sexism is one of those things that has always existed, and probably always will exist, but does seem to get a little better with time. When women couldn't vote, that was blatant sexism. When women are paid less than men for the same work, that's sexism. In school, when teachers call on boys more than girls, many people think that is an example of sexism. Sexism is similar to racism; they are both types of discrimination.