The Shiny Charm is available in Pokémon Black 2 and White 2. It is obtained by catching all of the Pokémon in the National Pokédex (excluding event-exclusive pokémon). It increases the likelihood of getting shiny pokémon.
What is the Shiny Charm?
The Shiny Charm is an item that, if you have it in your bag, increases the likelihood of finding shiny pokémon in the wild and hatched from eggs. The normal likelihood of finding shiny pokémon in the wild is 1/8192 (a 0.01% chance). Having the Shiny Charm in your bag improves this chance to 1/2730.6 (a 0.03% chance).
The Shiny Charm also affects the Masuda method. In Generation V, the normal chance of obtaining a shiny with the Masuda method is 1/1365.3 (a 0.07% chance). With the Shiny Charm in your bag, the chance is improved to 1/1024 (almost a 0.1% chance, i.e. almost ten times more likely than finding shiny pokémon in the wild).
How to Get the Shiny Charm
To get the Shiny Charm, you have catch to all of the pokémon in the National Pokédex, excluding the following event-exclusive pokémon: Arceus, Celebi, Darkrai, Deoxys, Genesect, Jirachi, Keldeo, Manaphy, Meloetta, Mew, Phione, Shaymin and Victini.
For Reshiram and Zekrom, as well as other version-exclusive pokémon, you can have a friend trade the pokémon to you, then you can give it back. The pokémon is considered "caught" even if it's no longer in your possession.
After you have caught all of the pokémon (except for the event pokémon mentioned above), talk to Cedric Juniper in Nuvema Town, then talk to Professor Juniper. She will give you the Shiny Charm.