Based on the word “intersection”, the word intersectionlaity signifies that each human belongs to more than one category and that the intersection between the categories can be more important than the individual categories – that the whole is more than the sum of the parts. Therefore, analysis that depends on one single categorization of people marginalize those who are already marginalized in more than one way. For example, black women will be marginalized not only in an analysis of sexism and gender oppression (which assumes that women are white), but also in an analysis of racism and racial oppression (which assumes that black people are men). It also shows that even when a social context typically treats a certain category as “privileged”, belonging to such a category can still be detrimental when it intersects with another category. For example: being part of a rich family is typically a privileged position, especially in a society which is conservative and has weak social infrastructure. Yet, being female and/or homosexual in this society can be bad enough if you are poor – but even worse if you are rich, with all the social expectations and family pressure which comes with it.
In a macro level social context where people are divided into many dichotomy categorizations where one category is the majority and the other category is the minority, everyone will end up being a minority person in one way or another: If a person actually happens to belong to the majority group in all categorizations, then this coincidence is rare enough to be a minority status in itself.
Actual intersectionality is about caring about everyone – caring about the actual persons who are part of categories, rather than merely caring about the abstract constructed categories themselves. By seeing that every person belongs to many categories and that these factors intersects with each other, we can start to study the complexities nuanced patterns as well as of each person's social situation. It may also be used to refute many cases of whataboutism. On the flip side, we have inverted intersectionality which is a kind of whataboutism dragged down to the personal level for each case of any problem - forming a bleak philosophy of hating everyone instead of caring for evryone.
Note that since intersectionality is very much about how categories interact with each other (or intersects each other, if yo will - this is the main idea, and it is also in the very name), the mere mathematical act of adding categories together should never be seen as being an act of actual intersectional analysis. This needs to be mentioned, since various versions of (mis)describing intersectionality as “assign numerical values to your categories and add them together to see of many points you get” has sadly gone viral on social media.