That is the sound of the filament (the part that lights up) breaking.
"Light bulbs which are aging or in bad condition generally fuse when they are switched on. This is because a tungsten filament (especially those which are worn out or thinned out) has low resistance to electricity when it is cold. When the current is switched on the filament is still in the process of heating up and building resistance, and so the filament breaks and the bulb fuses."
Light Bulb