Bitcoins are transferred between individuals or businesses by specifying their Bitcoin address. Transactions travel through the peer-to-peer network created by those who are running the Bitcoin client software.
There's no single point of weakness. Nobody can stop the Bitcoin system or censor it, short of turning off the entire Internet. If Wikileaks had requested Bitcoins then they would have received their donations without a second thought.
Of course, you should make of that what you will. You might also want to ponder the fact that practically anybody in any country can send and receive Bitcoins in an entirely unpoliced way.
Should your business be looking to accept Bitcoins? That depends on how valuable you think they are, of course, and that's going to depend on what you can get for the Bitcoins you accumulate--in terms of goods and services that can be bought for Bitcoins. The current Bitcoin-to-dollar exchange rate appears to be about 20 cents, and you can trade currencies courtesy of the various sites that let users both buy and sell Bitcoins.
However, purely as an intriguing idea that might indicate a possible future in an Internet heavily regulated by government, Bitcoins are worth taking a look at.
Keir Thomas has been writing about computing since the last century, and more recently has written several best-selling books. You can learn more about him at http://keirthomas.com and his Twitter feed is @keirthomas.
Sign up for CIO Asia eNewsletters.