To arrogate is to take over. When the teacher steps out of the classroom and some bossy student marches up to the chalkboard and begins scolding the other kids? The student is trying to arrogate the teacher's authority.
When someone takes control of something, often without permission, such as when a military general assumes the power of a country's government after getting rid of the previous leader, they arrogate power or control to themselves. Occasionally the verb arrogate means something like "assert one's right to," or take something that is deserved, but more often it implies a taking by force.