Wikipedia
Varmint rifle is an American English term for a small-caliber firearm or high-powered air gun primarily used for varmint hunting — killing non-native or non-game animals such as rats, house sparrows, starling, crows, ground squirrels, gophers, jackrabbits, nutria, marmots, groundhogs, porcupine, opossum, coyote, skunks, weasels, or feral cats, dogs, goats, pigs and other animals considered to be nuisance vermin destructive to native or domestic plants and animals.
The varmint gun fills a design gap between the more powerful big-game rifles and the less powerful rimfire firearms. .22 Long Rifle (the most popular rimfire caliber) is somewhat underpowered for small predators, but is perfectly adequate to dealing with typical vermin; the term "varmint" covers larger animals which usually harass farms from the outside (as opposed to infestation by vermin), and the varmint gun assists in the control of them.