Putting it coarsely, the issue is about the “you” person being selfish. Here are three examples, ranging from strong to weak to false.
Dad has hurt his back badly. It is a great effort for him to get out of bed to go to the toilet. He could drive a car to save his life, but otherwise it is out of the question.
His daughter’s weekly ballet lesson starts in half an hour. She rants for ten minutes about how she likes ballet, and how much she needs to go regularly in order to do well. She launches into a speech about how little Dad loves her. Dad replies gently, “It’s not about you.”
The point here is that, although the ballet is important, Dad has a problem that if far more significant.
A group of friends is going out to celebrate the birthday of one of them. They end up in a restaurant that does not have gluten-free food. One of them comments quietly to another that he is gluten-intolerant (which means that he won’t be able to eat anything). His friend replies, “It is not about you.”
The idea here is that it is a kind and generous act for the gluten-intolerant guy to not disrupt the celebration.
Daphne rings up Robert; she wants to see a movie, and wants someone to go with her. Robert apologises; he has an major assignment due in two days. Daphne abuses him for being uncaring and anti-social. “It’s not about you!”, she yells.
The idea here is that Daphne is just too focused on herself to see that Robert really can not afford to come to the movie.
The point of the expression, “It is not about you.”, is the implication that it is about somebody else (usually the speaker) — that what matters the most is some issue someone else has. As a rule, when someone says this, the “you” person does have a relevant issue; if the objection is correct, the point is that that issue is not as important as the issue the speaker has. Conversely, it can just mean that the “you” person is being selfish. (It is not that surprising if the speaker is actually being selfish (nor if the other party is being selfish and falsely believes that the speaker is being selfish).)
Note that, in the “weak” example, the idea is not that the issues involved are weak; the “you” person does have a legitimate objection, but the opposing issue — the birthday — is stronger.
I do not know the right terminology to label what it is that “it” refers to, as a grammatical concept. In everyday terms: it refers to the situation generally, and particularly to the issue that has given rise to the interpersonal conflict of interest [think “argument”].