A Catadioptric telescope has an optical tube assembly that uses a combination of mirrors and lenses. A common configuration is the Maksutov Cassegrain (Mak). This has a corrector plate (lens) at the front of the tube, in addition to the main mirror at the base of the tube.
Another type is the Catadiptric Newtonian. This has an additional lens in the focus assembly. In effect, it is a barlow lens that doubles the focal length of the tube without the extra size and weight of a long focal length OTA. The downside, is that there may be some slight loss of light gathering when compared to non catadioptric newtonian reflectors.
A good example of a Catadiptric Newtonian reflector is the Visionary Telesto 114mm newtonian reflector (see image)