I talk about it a lot, but have never had a serious pop at defining what the term means to me, so here we go. 

Patriarchy is about systems, not about individual people. It's about beliefs, attitudes, social structures, habits of behaviour and the like. Almost everyone living in a patriarchal system is a victim of this system - very few people actually benefit from it. Patriarchy hurts most men just as much as it hurts most women, and all gender-non-conforming people.

Patriarchy is a system based on power. It assumes that hierarchy and authority are always good and necessary. Where it gets especially problematic is that it assumes certain people are naturally supposed to have dominance over other kinds of people. That men are superior to women has been one of its hallmark notions. White supremacy over other races is part of this world view. Rich people are better than poor people, is another. Giving people power and authority based on merit is reasonable, giving it on the assumption that they should have power is as dysfunctional as it is prejudiced.

In a patriarchal system, hierarchies are enforced by threat, violence and fear. We're not taught why something is right, we're taught that certain behaviour will result in us suffering. It shows most clearly in how we treat vulnerable people, and especially children. Patriarchal systems demand obedience and unquestioning loyalty. Alongside this such systems glorify war and seek to replicate military structures in other areas of life.

Patriarchy is competitive. You're supposed to fight other people for a place in the sun. Manufactured scarcity contributes to it - capitalism is patriarchal. However, patriarchal systems deny the existence of unfair advantage and the way in which every competition is already biassed in favour of those already in positions of wealth and power. 

In a patriarchal system, all relationships are based on fear, control, ownership, power imbalance and the desire to get ahead. There's no room for gentler emotions - which are treated as both weak and feminine. The patriarchal male is supposed to cut off all feelings to concentrate on competing with other men for money, influence and power. 

At heart, a patriarchal system is one that depends on inequality in order to function. There have to be winners and losers and there have to be people at the bottom of the social pile for whom life will be hellish. Fear of becoming one of those people is a key tool for keeping people engaged in perpetrating the system. Hope of becoming a winner is also a motivator, but that's never a realistic option for most people.

If you don't believe that might is right, it looks like a pretty grim way to live.