...
is a phenomena which occurs when light propagates from the medium with greater index of refraction in the medium with lower index of refraction. From Snell's law we know that the light in this case refracts away from the normal. That means that there is an angle of incidence for incoming ray where all the light will not leave the medium with higher index of refraction, but instead it will reflect in direction perpendicular to the normal (i.e. in the plane of the boundary). If the angle of incidence is larger than this critical angle, all the light is reflected back into the medium with higher index of refraction. We can obtain value for critical angle mathematically using following equation:
Where n2 is index of refraction of the medium with higher index.
Image of multiple total internal reflections courtesy of Wikipedia. 
Practical Use of Total Internal Reflection
Total internal reflection has many practical uses. The best known are arguably its use in glass prisms in binoculars and cameras where it allows for compact size of the instrument while providing for long internal optical paths. Second major area of application is in optical cables - namely in multimode optical cables. There the pure glass/silica core is made of material with higher refractive index than the cladding that surrounds it and so the light which enters it under angle of incidence larger than critical it will reflect there and back thorough the cable to the other end (in the same way as on the picture above). This is used extensively in data communications as optical cables offer higher bandwidth (lower attenuation of high frequency signals), resistance to electromagnetic noise and (much) thinner cables.