One that focuses the incoming light with a mirror instead of a lens. One that gives inverted images of the objects seen through it. It is much easier to build and support large mirrors than lenses. Refracting telescopes cannot collect as many different kinds of light. Images produced by refracting telescopes are inverted instead of upright.
Stars stand out better in images produced by reflecting telescopes.
We get a larger magnification of the images. We get brighter, sharper images of astronomical objects. We can see a larger portion of the sky at the same time. They are not affected by atmospheric turbulence. The wavelength of the light.