noun
1. A system whereby addressable memory is extended beyond main storage through the use of secondary storage managed by system software in such a way that programs can treat all of the designated storage as addressable main storage.
SOURCE: Dictionary.com
EX. I've actually never turned to catch Zubats to keep from having to fight through them-- but I do have a box of Evee eggs in Heartgold. But let's talk about virtual storage for a moment...
I've gone over this sort of thing, in the past, when I talked about Pokéball technology but I think it's worth discussing how the PC boxes in the Pokémon series work. The Pokémon storage system was created by a young man who lives North of Cerulean City in the Kanto region named Bill (for Bill Gates of Microsoft), He called it the Pokémon PC and, in the games, it was labeled as Bill's PC. When you capture a Pokémon and already have a full party, you're given the option to put that Pokémon or another Pokémon you own in the PC (since six is the maximum party number) via the Pokédex transporter (I assume). You can also store and move Pokémon and items around in the PC box, usually at your local Pokécenter. In the anime, Ash tended to send his Pokémon to Prof. Oak (including a few dozen Tauros). The technology used in such a procedure is probably worthy of some thought.
Assuming that my theory about Pokéballs being correct, that is that Pokéballs are storage devices that render a Pokémon down into raw energy, copying their date, and re-synthesizing it later upon the release of the Pokémon (just like how Star Trek transporters work-- they destroy the subject and rebuild them), we can assume that Pokémon PCs are also virtual storage. The Pokémon being stored are destroyed, turned into energy, their information recorded, and, at a later date, you can re-synthesize them. The main difference is that the PC can store far more Pokémon.
As for why you can only carry six Pokémon, I haven't heard a legitimate reason for that...yet. We'll just have to leave that up for discussion at another time.
P.S. Pikachu knows the truth and doesn't want to be murdered for convenience-- even if he can and would be rebuilt and essentially be the same Pikachu. Hence, Pikachu's refusal to be put in his Pokéball.