PC is what is used to store Pokémon. It is an abbreviation for "Personal Computer."
History[]
The system was supposedly created by Bill. However, in in Generation III, a girl named Lanette says to have created/edited/modified it. The PC system was designed to put Pokémon that a trainer didn't have enough space for in his/her team. It has been seen in use in the anime, when Ash transferred his Pokémon to Prof. Oak to start a new journey into Hoenn without Charizard and the rest. It has 30 boxes in all the Pokémon games. The PC system also was used as a storage device to keep items for the trainer when they ran out of space. In the games, you can also check the Hall of Fame in the PC system when you have defeated the Elite Four and its champion.
Pokémon Bank[]
Pokémon Bank has since been revealed, in which players can place their Pokémon in a PC over the internet, and take them out when they are needed. It has been also revealed that you can store up to 3,000 Pokémon in up to 100 boxes. There will be an annual fee of $4.99/$5.