The simplest explanation is that the cartridge is what you put the game into when you want to play it on the actual hardware it was designed to be played in.
Think of Video Casette (VHS), or DVD disc When you want to watch video movie, then you go looking for a video cassete. Same thing when you are looking for a game to play on a handheld console, then you need a game cartridge. However, you may now exchange those cartridge with a flash card, so you can copy and delete the game via computer.
