A refractor telescope uses a converging lens, also known as a convex lens. This is how a magnifying glass works. The lens can offer magnifying power for a smaller telescope, but light does spread out do to refraction while it is inside the lens. Compound lenses can color correct to a degree.
A reflector uses a curved mirror to magnify the image. The color correction is not needed, but some other minor image distortions are possible. This is the telescope of choice by major observatories. It uses mirrors, at least one of which is curved to produce the magnification.
Another advantage the reflector has is that light does not pass through a lens. Some light is lost due to internal reflections when light passes through a lens as it does in a refractor. Another problem that is resolved is some frequencies of light are absorbed in the lens of a refractor due to hydroxide from water that cannot be fully removed in the glass making process. There is no absorption at the mirror of a reflector. Of course, no matter how highly polished a mirror is, some loss of light is experienced by a reflector, but this should be negligible.