The word "apocalypse" comes from the ancient Greek word apocálypsis, which literally means a revelation of truth. In practice it's any scenario which will cause drastic changes for the entire world/universe. There are different types of apocalypses involving demons, visions, angels and beasts. The apocalypse can also be caused by a natural disaster like an erupting volcano or a nuclear bomb. Something that's sure is that when the apocalypse hits, all or most of humanity is wiped out.
The apocalypse is a great setting for video games. The player may take control of a character who's trying to stop the apocalypse or who's trying to survive after said apocalypse happened. Some games like Shin Megami Tensei and Darksiders even let you take part in the apocalypse.
If an apocalypse reaches the point where absolutely nothing will survive after it, it is an Armageddon instead.