As light moves from one medium (say air) to another denser medium (say the glass of the prism), it is slowed down and as a result either bent (refracted) or reflected. The angle that the beam of light makes with the interface as well as the refractive indices of the two media determine whether it is reflected or refracted, and by how much (see refraction, total internal reflection).
Prisms are used to reflect light, for instance in binoculars, since they are easier to manufacture than mirrors. Prisms can also be used to break up light into its constituent spectral colors because the refractive index depends on frequency (see dispersion); the white light entering the prism is a mixture of different frequencies, each of which gets bent slightly differently. Blue light is slowed down more than red light and will therefore be bent more than red light.
Until Isaac Newton, it was thought that prisms added colors to white light. Newton placed a second prism such that a separated color would pass through it and found the color unchanged. He concluded that prisms separate colors. He also used a lens and a second prism to recompose the rainbow into white light.