The Battle.net Balance, AKA Bobby Bucks, was revealed in December 2011. This is Blizzard's term for the real currency balance tied to your Battle.net account. This money is used for purchasing items via the Diablo III Real Money Auction House, and can also be spent on other products from the Blizzard Store, including games, merchandise, and World of Warcraft fees.
The introduction of real money currency trading in Diablo III was a very contentious issue. While this article covers only the Battle.net Balance, you can find full details about the controversy in the Real Money Trading article.
Blizzard revealed this term and much of the explanation behind it in mid-December, 2011.
Paying in and Cashing Out
Players can add to their Battle.net Balance with credit cards or other online payment methods, depending on the region. The main purpose of such a balance is to buy items in the Diablo III Real Money Auction House. In some regions players will be able to pay for items directly with their credit cards or PayPal, without having to first transfer the money into their Battle.net Balance.
You can never directly withdraw money, though. All sales send the funds into your Battle.net Balance, which you can then withdraw from, in most, but not all, regions. Cashing out is not an option in all regions; some countries have laws regulating this (as the saga of the Korean Game Rating Board demonstrated).
In areas that allow cashing out, players can use PayPal to withdraw funds from their account, though PayPal charges their usual money transfer fee for this service. In regions that do not allow the cash out, players can only spend their Battle.net Balance on other products from the Blizzard online store. The balance is non-transferable in all areas, and Blizzard may delete your balance if an account has not been accessed in over three years.
See the Battle.net Balance FAQ for more details. Many specifics have not yet been revealed, and with terms varying so much in different regions, it will be essential to check Blizzard's info for your country, once that information is finalized.