A social system that values men more than women. Generally speaking, males are seen as the ‘real’ people, while women are less complete. It’s not unusual to find women are understood simply as ‘not men’ and so (arguably) not quite human. In English, the word men also means human beings – but women only means female humans – easy to see that the default human is a man.
In most contemporary societies white, youngish, rich & able heterosexual males are the most worthwhile people. Any deviation from that norm reduces a person’s value. Half the population is worth less because they’re female.
Naturally, a lot of people fall short of the patriarchal norm in more ways than one. We tend to lose privilege with each difference: a poor, elderly black woman with disabilities would come near the bottom of the pile. She’d find people don’t much care what she has to say, and they forget to factor in her needs when making plans. It would be very hard for her to improve her position by earning more because she’s not valued. A fairly new field of study, intersectionality, looks into the effects of overlapping social disadvantages.
A feminist talking about “the patriarchy” doesn’t mean there’s a Patriarchy Committee somewhere, making the rules! It’s just that we live in this system, we all know the rules, and we can change them – because, as a society, we make them. We take them for granted, but we can change them.