Call me a sperg but I find the definition the LGB Alliance provides to be plenty helpful:
"gender identity:
Like “transgender,” gender identity is defined many different ways by its proponents. It typically describes one’s personal sense of being male or female or neither, regardless of one’s actual sex. Since male and female are material reality and not feelings, “gender identity” is based on gender stereotypes. Since these vary across time and cultures, it is difficult to provide a concrete definition of the term, especially as new “genders” are regularly invented that seem to have nothing to do with sex or even necessarily gender roles, but rather serve as labels to express one’s personal interests or characteristics. We prefer to call this “personality.”"
So basically, just sex-based stereotypes in my opinion. Gender identity is absolutely unnecessary in the western world but it makes people feel special and oppressed, so there's my two cents.