A reflector telescope is one of two general categories of telescopes: optical or binocular. They differ in the way that the light is reflected rather than being reflected off of a particular object. Reflector telescopes use an objective lens to focus light onto a receiving lens, so all of the light rays have an associated wave that reaches the receiving lens. The reflecting telescope was invented in the late 1890s and is commonly used by amateurs. Reflector telescopes are usually more expensive than other types of telescopes and are not appropriate for all situations.
A reflecting telescope is made up of two parts: a primary mirror, and a secondary mirror. The primary mirror passes through an objective lens at great speed, creating its own image. The secondary mirror is slowed down by lenses and mirrors so that it mirrors the primary mirror on its own. This creates an image that is the same size as the primary mirror, but with a wave of slightly bent light passing through the Secondary Mirror and reflecting back onto the primary mirror which causes it to reflect the light.
Although reflectors are generally much cheaper to manufacture than refractors, they don't have nearly the same lifespan. A reflecting telescope can last for centuries, but a refractor will need to be replaced after about ten years of use. Reflectors also cost less money to operate, but they need to be cleaned and maintained very often to keep their effectiveness. The fact that refractors do not throw off any particles makes them the better option if you do not wish to be bothered with cleaning, maintaining and operating your telescope.
Another important difference between reflectors and refractors is the fact that a reflector has no image tube. The light that passes through the primary mirror (which acts as the reflector) is sent through a narrow path that produces a reflection. Because the mirror is only a single line of glass, the reflector has very clear edges. A refractor telescope has many different edges, which can cause some of the light to go through and be reflected on either side of the primary mirror. This causes a variety of "culling" effects, making the telescope less accurate at resolving details.
Reflectors also are great if you want to study heavenly objects at night. When a light from an object reflects off of a mirror, the resulting image is seen as a faint glow on the edge of the primary mirror. Since the moon, planets, stars, and other celestial objects are spread out over vast distances, you can see the effect even with a large telescope. Since the secondary mirror acts as the focus of this glow, it magnifies the image and creates a clearer outer surface. Because reflectors have no image tube, you also get a larger diameter than a refractor, which means you'll be able to use them for greater magnifying capabilities.
Reflector telescopes are most commonly used in research and observation programs. They make it much easier for people to observe heavenly objects during research projects that require them to travel long distances to get a close-up look at a specific object. You can also use a reflector to help monitor the integrity of your primary mirror. A reflector also lets you use small "deward" mirrors to check for wobble while your primary mirror is free spinning.