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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