A word used to introduce a hypothetical assumption. "If I had a dog..." is equivalent to "I don't have a dog, but assuming that I did..."
If is usually followed up at some point with a "then", although sometimes this is left implied. "If I had a dog, THEN I'd be cool.", or perhaps, "If I had a dog, I'd be cool."
If (often IF) is also the common name used for If: Worlds of Science Fiction, a science fiction magazine that published short stories and novellas from 1952-1972. The name changed in 1972 to Worlds of If. Under the new title IF continued until 1986, but during the years 1975-1985(!) no issues were put out.
IF was the first to get hold of Keith Laumer's Retief stories and Fred Saberhagen's Berserker stories. IF also had some big name editors; Frederick Pohl, Damon Knight and Horace Leonard Gold.