As with many disc using games, data was either saved on internal memory or on a memory card. Unlike the Nintendo 64, the Nintendo GameCube was very dependent on the memory card. However, there was an unofficial accessory released in 1998 to allow users to transfer saves onto their computer known as the DexDrive, bypassing the need to buy multiple Controller Paks. Each Controller Pak is 32 kilobytes, making each page 256 bytes. Most Controller Paks could only hold up to 123 pages of memory, 128 total, making 5 pages reserved for formatting purposes.
An example of this was Mario Kart 64, where all race data was saved onto the game, but Ghosts from time trials were saved onto the Controller Pak.
Many games just used the Controller Pak for storing non-main game data. The Controller Pak, however, wasn't necessary for many games as the cartridges that the system used allowed for data to be directly saved onto it (much the same as the cartridges for the Game Boy). It plugged into the controller's accessory slot. However, it's actually called the Controller Pak by many games. The Nintendo 64 was the first Nintendo system to have a memory card. The Nintendo 64's Controller Pak (front and back)