To give an actual video game example.
When making a computer program, you have to constantly insert and remove things into and out of memory. The removal of unused information in memory is called 'garbage removal'.
Basically a memory leak is caused when information that is no longer needed is not being removed from memory, and eventually leaves very little memory for the rest of the program to use.
So say in Skyrim a dragon appears on screen, that dragon then takes up a hunk of memory. The memory should only be used until that dragon is no longer a relevant piece of information, at which point it is removed from memory.
The issue occurs when the dragon isn't removed from memory, and you run out of room to put new dragons in
