Mirror Lenses are lenses typically used to reach out to long focal lengths with lower cost and smaller/lighter size. They can be extremely small for a lens of their focal length. Unfortunately they usually have extremely small maximum apertures- f/8 or f/11.
The major manufacturers often have their own, like Nikon and Canon, but these were primarily in the manual focus days. Now you see them more often as generic brand on ebay.
The primary complaint I see besides the max aperture being so slow is the bokeh. Mirror lenses have a primary mirror that focuses the image to the second mirror in the center of the front of the lens which in turn focuses it on to the image plane. As a result, point highlights in the out of focus areas of the background instead of being rendered as blurry points of light like with a normal lens, they are rendered as 'Doughnuts' because there is a dark center like the hole in a doughnut. Visually this can be slightly distracting at times.
Otherwise they are economical ways to get out to long focal lengths at a low price and without breaking the back.