In Pokemon Red/Blue (USA, I'm assuming in other gen 1 releases as well), you can carry 6 pocket monsters with you at once. Extra ones are stored in "boxes" on the computer. If you have 6 and catch a wild monster, it is sent to the box automatically. However, each box can hold only a few pokemon. After the box is full, when you catch a wild one, the game gives an error message that you can't catch this one because the box is full. If you go switch to another box, the game says it has to save before switching.
Why is this?
I assume there is some kind of hardware limitation related to writing to the SRAM, or in the bankable RAM where data is loaded, but I would appreciate a more detailed explanation.