There are many different types of mirrors, and each behaves somewhat differently. The most common type is a silver mirror, consisting of a thin layer of silver on the bottom side of a glass slide. Additional layers of copper or other materials may be deposited on the back side of the silver layer, but these layers are not relevant for the optical properties.
To understand how such mirrors work, let us first describe the interaction of light with some media in the semiclassical view. Light consists of electromagnetic waves, which induce some oscillation of electrons in any substance hit by the light. In an insulator such as glass, the electrons are firmly bound and can only oscillate around their normal position. This movement influences the propagation of light so that its wave velocity is reduced, while there is only a small loss of energy. This is different in a metal, where some of the electrons are free to move over large distances, but their motion is damped so that energy is dissipated. The wave amplitude decays very quickly in the metal--usually within a small fraction of the wavelength. Associated with that decay is a loss of energy in the wave and some heating of the metal. Most of the incident optical power, however, is reflected at the air/metal interface. In other words, the power is transferred to another wave with a different propagation direction (opposite to the original direction for normal incidence on the surface).
In the case of a silver mirror, this reflection occurs at the interface of glass to silver, essentially because the optical properties of the metal are very different from those of glass. (As a general rule, waves experience significant reflection at interfaces between media with substantially different propagation properties.) In the case of this silver mirror, there is also another, weaker reflection at the air/glass interface. In the end we obtain a reflected wave with essentially the same properties as the incident wave apart from some loss of power, which typically amounts to a few percent for silver mirrors.
This reflection loss does not matter for a mirror used in the bathroom, but such metallic mirrors are usually not suitable for use in lasers. The loss of light itself is often unacceptable, and the associated heating of the mirror can cause difficulties, in particular via thermally induced deformations. These affect the spatial properties of the reflected light. For example, bulging of the mirror surface can defocus a laser beam.
Other types of mirrors, so-called dielectric mirrors, are superior for use in lasers. They consist only of nonconductive materials (insulators), typically with an alternating sequence of thin layers. For example, a sequence of 15 pairs of silica (SiO2) and titanium dioxide (TiO2) layers--each having a thickness of a few hundred nanometers--deposited on some glass substrate can serve as a highly reflecting mirror for laser applications. Here, the reflection at each single interface of two layers is rather weak, but dozens of such reflections are superimposed to obtain a high overall reflectivity. Such mirrors can easily reflect more than 99.9 percent--in extreme cases even more than 99.9999 percent--of the optical power. A noteworthy feature of dielectric mirrors is that they are highly reflecting only for light in a very limited range of wavelengths. If this wavelength range is located in the infrared region of the optical spectrum, such mirrors may not even look like mirrors, since they allow most of the incident visible light to pass through. Dielectric mirrors may also be designed for special purposes--for example, to reflect 80 percent of green light while transmitting nearly 20 percent and simultaneously to transmit red light nearly completely. Certain mirror designs even allow temporal compression of ultrashort pulses of light to even smaller durations, such as a few femtoseconds (one billionth of one millionth of a second). This effect is related to tiny wavelength-dependent time delays that light experiences in the mirror structure.
In a quantum-mechanical picture, light consists of photons, or packages of optical energy. The photons of the light reflected from a metal (or a dielectric mirror) are identical to the incident ones, apart from the changed propagation direction. The loss of light in the metal means that some fraction of the photons are lost, while the energy content of each reflected photon is fully preserved. Which of the photons are lost is a matter of chance; there is a certain probability for each photon to be absorbed. So if one illuminates a metal with a source of single photons, there will be complete reflection (and no heating of the metal) in most cases and complete absorption with associated heating (creation of so-called phonons in the metal) in some cases.