In effect, Battle.net Balance is a virtual wallet where players can purchase -- or "charge up" according to Blizzard's parlance -- points to then spend on items and services in World of Warcraft, Diablo III, and elsewhere. Diablo III players who earn Battle.net currency in-game can save those points through the service to spend later. The system can also be used to pay for WoW gametime.
However, the system comes with an important caveat: Once you've converted real-world money into Battle.net Balance, there's no getting it back as cash. So if you've got plans to make a living playing Diablo III, you might want to think again (although "certain regions" will be able to cash out via PayPal).
Battle.net Balance is heading our way in the near future, and if this affects your game, you might be interested to read the informative FAQ that goes into more detail.