Assuming you mean the old filament type incandescent lights. The filament gives off light when it heats up. Resistance increases as temperature increases. Current decreases when resistance increases. So when you first turn on the light, when the filament is cold, is when the filament has the lowest resistance and sees the greatest current.
This initial current can be what causes the filament to burn out. In truth it is a bit more complicated – because the degradation over time is not even throughout the filament, so there will be “weak spots” that when a high current tries to push through, it causes a very local high temperature that can cause a “catastrophic” burn out of the entire filament.