Bitcoin is a form of virtual money, which was created in 2009. The units of the money are called Bitcoins and are decentralized drawn and managed in a computer network. This network is made up of participants who run a Bitcoin client and connect to each other via the Internet.
The official Bitcoin logo
Bitcoins can be transferred electronically as required between the participants. Your ownership is evidenced by the possession of cryptographic keys. Each transaction of monetary units is provided with a digital signature and recorded in a public, run by the entire network database.
The units of money can be exchanged at online exchanges against other currencies.
You can accept Bitcoins as payment for goods and services, or buy them from a friend or someone in the area. You can also buy directly on a stock exchange.
A personal note:
If you like to buy some bitcoins for example at btc-e.com you have to keep in mind that you cannot withdraw your bitcoins immediately after the purchase.
For anti-fraud purposes the stock exchanges want to see a copy of your ID and a electricity or hydro bill as a proof for your identity. When i bought some coins at btc-c.com it lasted up to 3 days before i was able to withdraw my bitcoins into my personal digital wallet.
If you want to have an additional layer of security for your Bitcoins you can use a paper wallet so your coins are not stored on your personal computer, and only available with a code you have printed on a piece of paper.
If you have any questions regarding Bitcoins or Litecoins feel free to comment here.
(A Litecoin is another digital currency which works very similar)