Shinwari,Mariam,Ivan text:
Total Internal Reflection
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. Optical cables are also used in endoscopes (stomach sonds). Other uses are for example in inkless fingerprint readers.
In daily life it is easy to demonstrate total internal reflection for example by looking upwards when underwater - you will be able to see a cone of your surroundings (areas where angle of incidence is lower than critical) and reflection of other underwater object everywhere else (where angle of incidence is higher than critical). In other (much simplified) words: when underwater the water surface will in some cases work as a mirror (due to total internal reflection).
Dispersion of Light
The index of refraction of medium is dependent on the frequency of incoming light ray. Therefore if light with with wide frequency spectrum (such as daylight) enters for example glass prism, the component frequency bands (for visible colors) will diffract under slightly different angles. The result is light divided into colorful "strip" for each of basic colors. The very same effect is behind rainbow which is natural occurrence of dispersion.
Diffraction of light in prism courtesy Wikipedia: 
Practical Use of Dispersion
Dispersion is used in spectrometers - devices which are used in many fields of science to analyze the chemical composition of objects. It is based on the fact that different chemical elements emit and absorb different wavelenghts of light, and this spectra can be seen using spectrometers.
In other fields, the dispersion can be a nuisance: in camera lenses it leads to chromatic aberration and in optical cables chromatic dispersion limits the maximum bandwidth of the fiber (though this effect is not as strong as modal dispersion which is caused by longer paths of reflected rays as opposed to those that travel straight through along the core).
Further Reading/Watching