The incandescent light bulb contains a thin coil of tungsten wire called a filament. This coil has a very high resistance to electricity. When electric current flows through it, it produces heat---in fact, it becomes "white hot." When any metal becomes this hot it combines with the oxygen in the atmosphere and burns up. To prevent this, all of the air is removed from the light bulb and is replaced with an inert gas such as argon.
If the light bulb is poorly sealed during manufacture or becomes cracked during handling, air will leak into it. The filament will oxidise and burn up, causing the bulb to blow out.
Tungsten is a brittle metal and when drawn into a fine wire it becomes very delicate. When light bulbs are jarred or dropped, the filament can either break completely or become cracked. The bulb will either no longer work, or the filament will quickly fail at its weakest point.
The most dramatic example of a light bulb "blowing out" is when lightning strikes a power line or transformer near your home. The sudden spike of high voltage is more than the filament can handle and it immediately burns up, sometimes bursting the bulb.
Early light bulbs contained no atmosphere---a vacuum. Because of the reduced pressure inside, the hot tungsten wire would evaporate relatively quickly, resulting in premature failure of the bulb. Filling the bulb with inert gas, at nearly atmospheric pressure, reduces this evaporation.
The most common reason for the failure of a light bulb is what occurs during its normal use. At high heat, the atoms of the tungsten filament will still slowly evaporate into the argon atmosphere of the bulb.This evaporation is almost imperceptible. However, the filament eventually gets thinner and weaker until it burns through at its weakest point, sometimes with an audible "pop." The light bulb reaches the end of its useful life and "blows out."