Fumigation is the process of using chemical smoke to kill pests like insects or rodents. An infestation of termites in your house might mean you have to resort to fumigation.
Because fumigation fills the air with poison gas, it's a process that has to be done in an empty space — in other words, you'll have to leave your house and bring your cats with you during fumigation. Today this noun refers specifically to pest control and the use of pesticides in the form of gas or smoke. The original 14th-century definition was "action of making aromatic smoke as part of a ceremony," from the Latin root fumus, "smoke."