The links provided by Mike do a good job, but I'll attempt a more "simple" explanation.
A regular camera lens is made of transparent glass that lets light pass through, but bends its trajectory to form an image. That process is called refraction, so a regular lens is refractive.
A mirror lens does not use refraction but reflection. That means instead of transparent elements, the lens will have reflective elements (mirrors). Those mirrors are curved and also change the trajectory of light, again to form an image. Most high-quality telescopes are, in fact, mirror lenses (Hubbles is one example).
Here is a drawing of the general design of mirror lenses, it's also called a Cassegrain telescope:
In theory, mirror lenses are better at sharpness and contrast, because light never enters any glass element, so is not likely to be absorbed or modified. In practice, mirror lenses are worse for bokeh (the out of focus texture quality) and are often, sadly, of average quality.
I hope this helps.
