The verb infest means to invade in large number, often resisting control and causing damage or hardship. Bedbugs can infest people's belongings and even their bodies, or mice may infest your kitchen if you leave the cheese out too often.
Infest comes from Latin: in- means "not" and festus means "able to be seized." So infest describes something is not able to be seized, typically because it's present in such large numbers. For example, mosquitoes may infest your backyard during the summer and annoy you when you're trying to relax. Infest is usually used to describe pests, such as bugs or rodents, that overrun something in such large number that they are difficult to control.