A mirror is a reflective surface that is smooth enough to form an image. The best known example is the plane mirror. The most common use is in the home for shaving, make-up etc but mirrors are also used in scientific apparati such as telescopes and lasers, and in industrial machinery.
In a plane mirror, a parallel beam of light changes its direction as a whole, whilst still remaining parallel; the images formed by a plane mirror are virtual images, of the same size as the original object (see mirror image). There are also parabolic concave mirrors, where a parallel beam of light becomes a convergent beam, whose rays intersect in the focus of the mirror. Finally, there are convex mirrors, where a parallel beam becomes divergent, with the apparent intersection occurring behind the mirror. Note that spherical concave and convex mirrors do not have a single focal point, as often described in high school physics text books (see spherical aberration in Lens (optics) and Aberration in optical systems).
A beam of light reflects off a mirror at an angle of reflection that is equal to its angle of incidence. That is, if the beam of light is shining on a mirror's surface at a 30° angle from vertical, then it reflects from the point of incidence at a 30° angle from vertical in the opposite direction.
Contrary to popular belief, mirrors do not actually reverse left-to-right; they actually reverse front-to-back. Light rays reflecting off a mirror have their front-to-back direction reversed, while the left-to-right and top-to-bottom components of their direction remain unchanged. The confusion comes from the perception that if a person were standing behind the mirror facing us, as our reflection seems to, then they would be reversed left-to-right relative to ourselves. However, this left-to-right reversal is not performed by the mirror, but rather by this imaginary person turning around left-to-right to face us from behind the mirror.
Most modern mirrors consist of a thin layer of aluminium deposited on a sheet of glass. They are back silvered, where the reflecting surface is viewed through the glass sheet; this makes the mirror durable, but lowers the image quality of the mirror due to extraneous reflections from the front surface of the glass. This type of mirror reflects about 80% of the incident light. The "back side" of the mirror is often painted black to completely seal the metal from corrosion.
Viewing one's own body
A mirror is used for inspecting parts of one's body which are difficult or impossible to see directly, such as the face, neck or the whole body. This may be to check physical appearance (including clothing, make-up, hair, etc.) or to control applying make-up, shaving, cutting hair, fixing one's tie, etc.
Telescopes and other precision instruments use front silvered mirrors, where the reflecting surface is placed on the front surface of the glass, which gives better image quality. Some of them use silver, but most are aluminum, which is more reflective at short wavelengths than silver. All of these coatings are easily damaged and require special handling. They reflect 90% to 95% of the incident light when new. The coatings are typically applied by vacuum deposition. A protective overcoat is usually applied before the mirror is removed from the vacuum, because the coating otherwise begins to corrode as soon as it is exposed to oxygen and humidity in the air. Front silvered mirrors have to be resurfaced occasionally to keep their quality.
The reflectivity of the mirror coating can be measured using a reflectometer and depends on the wavelength of light as well as the metal. This is exploited in some optical work to make cold and hot mirrors. A cold mirror is made by using a transparent substrate and choosing a coating material that is more reflective to visible light and more transmissive to infrared light. A hot mirror is the opposite, the coating preferentially reflects infrared. Mirror surfaces are sometimes given thin film overcoatings both to retard degradation of the surface and to increase their reflectivity in parts of the spectrum where they will be used. For instance, aluminum mirrors are commonly coated with magnesium fluoride. The reflectivity as a function of wavelength depends on both the thickness of the coating and on how it is applied.
For scientific optical work, dielectric mirrors are often used. These are glass (or sometimes other material) substrates on which one or more layers of dielectric material are deposited, to form an optical coating. By careful choice of the type and thickness of the dielectric layers, the range of wavelengths and amount of light reflected from the mirror can be specified. The best mirrors of this type can reflect >99.999% of the light (in a narrow range of wavelengths) which is incident on the mirror. Such mirrors are often used in lasers.
Safety and easier viewing
Rear-view mirrors are applied in and on vehicles (such as cars, or bicycles), to allow drivers to see other vehicles coming up behind them.
Some motorcycle helmets have a built-in so-called MROS (Multiple Reflective Optic System): a set of reflective surfaces inside the helmet which together function as a rear-view mirror  (http://www.reevu.nl).
There exist rear view sunglasses, of which the left end of the left glass and the right end of the right glass work as mirrors.
Rounded mirrors are sometimes placed at corners of places such as parking lots or stores, allowing people to see around corners to avoid crashing into other vehicles or shopping carts.
Mirrors are also sometimes used as part of security systems, so that a single video camera can show more than one angle at a time.
A one-way mirror, also called two-way mirror (!), reflects about half of the light and lets the other half pass. It is a sheet of glass coated with a layer of metal only a few dozen atoms thick, allowing some of the light through the surface (from both sides). It is used between a dark room and a brightly lit room. Persons on the brightly lit side see their own reflection -- it looks like a normal mirror. Persons on the dark side see through it -- it looks like a transparent window. It may be used to observe criminal suspects or customers (to watch out for theft). The same type of mirror, when used in an optical instrument, is called a half-silvered mirror. Its purpose is to split a beam of light so that half passes straight through, while the other half is reflected -- this is useful for interferometry.
With the sun as light source, a mirror can be used to signal, by variations in the orientation of the mirror. The signal can be used over long distances, possibly up to 60 kilometers on a clear day. This technique was used by Native American tribes and numerous militaries to transmit information between distant outposts.