To fumigate is to spray something with fumes, usually to eliminate pests of some kind.
A fume is a type of smoke or other gaseous substance, and fumigation is when fumes are used to treat something. Most of the time, a house is fumigated because it has pests in it. If you have cockroaches or bedbugs, you might need to fumigate. Fumigating is a gaseous chemical attack that kills pests and is also dangerous to people and pets, so people clear out before fumigating takes places. The person who fumigates is usually an exterminator.