Intersectional feminism is a term that is intended to specify that the feminism being discussed is one rooted in recognizing that there is a combination of different types of discrimination and oppression each woman faces based on their demographic factors.
For example, an intersectional feminist will consider and look at the different layers of discrimination based not only on sex, but on gender identity, race, ethnicity, ability vs disability, sexual orientation, age, etc.
The importance of specifying that one is an intersectional feminist, is because historically, the concerns of feminism have been the concerns of white women. When feminists talked about their struggles, the talk was about the struggles of white women as though this was the universal experience of all women. But we know that this is simply not true and tends to either obscure the experiences of non-white women and/ or reinforce racist ideas.
This term was coined by Kimberlé Crenshaw in 1989 to describe the specific oppression of African-American women, which was unique given the intersection of their gender and their race.
Again, just because women as a whole have been oppressed by a patriarchal society and have faced misogyny, does not prevent us from internalizing and perpetrating other forms of oppression and discrimination. Therefore, it is important to begin to name each of the various layers of experience and oppression a person has and try to understand their experience from that perspective.