Where does the rat terrier's breed name come from?

"Named by the perceptive Teddy Roosevelt, the Rat Terriers were developed in Great Britain originally from Smooth Fox Terriers and Manchester Terriers in 1820. They were brought to the USA in the 1890's. At that time they were all their original color of black and tan. Life Magazine showed President Roosevelt with three black and tan Rat Terriers. American breeders crossed them again with the Smooth Fox Terrier as well as the Beagle and Whippet. The Beagle increased bulk, trailing and hunting ability, along with the red color. Whippet contributed the speed and agility and probably the blue and brindle colors. The smallest variety was derived from the Smooth Fox Terrier and Chihuahua. The Rat Terrier proved to be one of the best in the rat-baiting pits. One Rat Terrier is reported to have killed over 2,501 rats in a span of only seven hours in a rat infested barn. The Rat Terrier is a hard-working farm hand, able to rid an infested barn of vermin with no problem."

The name came from the fact that is used to hunt and keep Rats and other Vermin under control in human-populated areas. The terrier part comes from the group of dogs that go after vermin in the ground, (terra in latin means Earth). These dogs originally came from Britan, like the answerer above said.

Hope that helps!