Sex is physical. There are more than two sexes. Some examples are female, hermaphrodite, and male (among others).

Gender is social. There are more than two genders. Some examples are masculinity, femininity, and androgyny (among others).

Edit: (expanding upon the above)

Sexuality is social. There are more than two sexualities. Some examples are heterosexuality, homosexuality, and bisexuality (among others).

A person's sexual identity is the triplet defined by these three items. For example, one could be an androgynous male homosexual.