Total internal reflection is an optical phenomenon. When light crosses materials with different
refractive indices, the light beam will bent at the boundary surface (i.e. refraction). At a certain angle of incidence (the critical angle), the light will stop crossing the boundary but instead reflect back internally at the boundary surface.
This physical property makes optical fiber useful and the rainbow in the sky and roof prism binoculars possible.
See also Snell's Law, Fresnel equations.
To see an animation of the effect, go [here] and click and drag the mouse pointer.