In a monarchy, if the king gets too sick to rule his country, a regent steps in to run things temporarily.
When kings or queens aren't able to do their jobs — because they're ill, or often because they are children — trusted advisers called regents fill in. You can think of a regent as a substitute monarch. There's also a more permanent kind of regent who helps to run a business or university and can also be called a trustee or board member. In Latin, regent means "ruling," from the verb regere, "to rule."