Definitions of Reflector and Refractor.

Refractor: Refracting telescopes use lenses to gather light. (Lenses refract, or bend, the light.) Whether or not Galileo actually developed the first refracting telescope, he was certainly the first one to turn such a device on the stars. (He might have gotten the device from regional merchants.) The Yerkes 40-inch refractor is the largest refracting telescope in the world.
Reflector: Reflecting telescopes use mirrors to gather light. (Mirrors reflect the light.) Reflectors were developed by Sir Isaac Newton in the 17th century. The mirrors in these telescopes are curved and shallow.
There are several reasons why most modern research telescopes (and the biggest telescopes) are reflectors.

The Royal Observatory Greenwich in the UK has a nice collection of leaflets, including one on telescopes that discusses several types of telescopes if you would like to know more. (It even mentions Yerkes!)

Nick Strobel's site has a nice article about telescopes.