The conventional categories of identity politics are race, sex, gender, sexual orientation, ethnicity, class, age, etc. In each of these categories, some identities are privileged while others are discriminated against. But a particular individual exists within multiple categories and thus holds multiple identities. Each identity has its own place on the spectrum of privilege or discrimination hierarchies. They “intersect,” and so a person’s “intersectionality”–that is, the particular combination of identities–defines his or her position on the socio-political hierarchy.
A black man who is heterosexual and middle class is oppressed because of his race, but his sexual orientation and social class are privileged. A white woman who is lesbian and working class is privileged for being white, but her sex, sexual orientation, and social class make her oppressed. A black, transgendered, lesbian, working class woman is more oppressed.
With intersectionality, you may be privileged, but you have areas in which you are oppressed. Or if you are oppressed, intersectionality helps you to see that there are people even more oppressed than you are.
Intersectionality theory offers a complex calculus for calibrating how oppressed a person is, and thus who has the highest moral high ground within a group of leftists. This explains a lot, as I get into after the jump.