Bitcoin is a new currency that was created in 2009 by a gentleman using the screen name Satoshi Nakamoto. No one really knows who he is. (Giving you lots of confidence already, right?
)
Bitcoins are "created" by mining them - using a computer to solve complex mathematical equations, and those equations are actually an ongoing ledger of Bitcoin transactions throughout the world. Miners are "rewarded" with a small percentage of the coins they mine.
You can buy bitcoins with cash, exchange them with other people or acquire them by accepting them in your business. It's a valid currency that offers several advantages over fiat currency, namely you remain anonymous in all of your transactions, there are no banks or regulating agencies involved and the security is very high-level.
You can "play the market" with bitcoins - there are over 100 other alternate currencies at this point, and you can speculate by buying those currencies and holding them in hopes of their becoming popular. You can also hold your bitcoins and sell them when their value increases, but of course there are also decreases, so like the stock market it's a form of gambling.
You store your bitcoins in a "wallet", basically a tiny text file on your computer that contains your "address" - for example, my public address is:
19vKdk8KxdLNQ3SXrsx8vWELv96pagKoJd
So if anyone wanted to send me bitcoins they would just use that address and voila, the coins would appear in my wallet. (Hint, hint!)
Of course I have a private address, multiple passwords, two-phase verification, etc. - all security methods designed to protect my virtual currency.
You can also earn bitcoins by doing small online jobs such as surveys, or you can visit one of the hundreds of "faucets" which periodically "leak" a tiny percentage of bitcoin, which is then credited to your wallet.
Hope that helps at least a little - I'm still learning all the ins and outs of the currency myself, and it's a fascinating study.