Catadioptric telescopes work on the same primary principle as the reflecting telescope. However, before light travels to the objective mirror it is first filtered through a correcting lens. This allows images to be produced in a shorter telescope than would be required in a reflector, so that you can increase aperture while not getting too large of a telescope.
Choosing the Telescope That is Right for You
In order to know what telescope is the right purchase for you, you should ask yourself a few questions. First and perhaps most importantly: how interested are you in astronomy? A telescope is a major purchase, although one can be purchased for about a 100 or 150 dollars, most telescopes that are going to prove worthwhile will run in at least the 300 dollar range, and only go up from there.
If you are interested in astronomy, but perhaps not that interested, there are other options. Even viewing the stars with the naked eye can be enjoyable. One can also purchase excellent binoculars for less than the cost of a telescope that will allow increased viewing of the stars without requiring a major monetary commitment.
How much do you want to see? Your ability to see with your telescope will depend greatly on the size of the aperture of your telescope. Refracting telescopes, for example, offer the sharpest image for the amount of aperture they provide, however they do not (and cannot) offer very large apertures, because they would be far too large and bulky past a certain point. However, a small refracting telescope can be great for casual viewing of the moon, the planets and double stars, but will not offer much in the way of deep space viewing.
Reflecting and catadioptric telescopes offer much larger apertures, however these larger apertures are also going to prove to be more expensive.