Kyriarchy is a big word that helps people understand how different systems of power and oppression (when some people have more power and control than others) are connected to each other. Imagine a big tower made up of smaller towers that all support each other.
At the very top of the tower is the most powerful group of people - usually men, white people, cisgender people, heterosexual people, and people who have a lot of money. These people have a lot of control over how things are done in society, like who gets to be in charge, who gets to make the rules, and who gets to have the most money.
The people at the top of the tower benefit the most from the way things are structured, because things are set up to support them and give them more advantages than anyone else.
But the tower wouldn't work if it was just one group at the top. Instead, there are many smaller towers that support the big tower, each representing different forms of power and oppression. For example, there might be a tower for racism, a tower for sexism, a tower for homophobia, and so on.
Each tower has people in it who benefit from that particular kind of power and oppression. For example, in the tower of racism, white people have more power and control because of the color of their skin. In the tower of sexism, men have more power and control because of their gender.
The towers all work together to keep things the way they are, with the same people at the top and the same people at the bottom. If any one tower were to fall, it would weaken the whole system and challenge the power of the people at the top.
Kyriarchy is a way to understand how all of these different towers of power and oppression work together, and to help us figure out how we can change the system to make it more fair for everyone.