PokeGen is a Pokemon data editor for Generation 4 and 5 games
(DPPtHGSSBW). It works from a computer and can interact with a game by
using one of these: an Action Replay, a flashcart, or a GTS sending
program. Raw PKM files can be saved and edited in all current formats
(encrypted, decrypted, 136 byte and 236 byte), and new files can be
made from scratch.
PokeGen focuses on making Pokemon editing easy, while still keeping
Pokemon legal in terms of the game itself. Pokemon generated by other
programs are more likely to look "hacked" than a Pokemon generated
Basically, it is an unofficial site that creates or "gens" Pokemon, meaning that you can edit nicknames, EVs, IVs, Hidden Power types, shininess, the whole package, and then send them to a Generation 4 or 5 game.
It is not related to Pokebank in any way, as that is an official storage program run by Nintendo, however, many people talk about sending "genned" Pokemon through the bank, because they are widely regarded as the only way to get hacked Pokemon into the game, apart from high-level hacking.