Bitcoin is a currency, obviously. Just like USD and the likes. But the reason Bitcoin is such a big deal is because its the first of its kind, a completely digital currency. You might think of PayPal as a digital currency, but it isn't as it has the backing of real currencies unlike Bitcoin. Bitcoin is a crypto currency, meaning its completely anonymous.
For how the economy works, check out the Bitcoin wiki. Here's a quote:
Where does the value of Bitcoin stem from? What backs up Bitcoin?
Bitcoins have value because they are useful and because they are scarce. As they are accepted by more merchants, their value will stabilize. See the list of Bitcoin-accepting sites.
When we say that a currency is backed up by gold, we mean that there's a promise in place that you can exchange the currency for gold. Bitcoins, like dollars and euros, are not backed up by anything except the variety of merchants that accept them.
It's a common misconception that Bitcoins gain their value from the cost of electricity required to generate them. Cost doesn't equal value – hiring 1,000 men to shovel a big hole in the ground may be costly, but not valuable. Also, even though scarcity is a critical requirement for a useful currency, it alone doesn't make anything valuable. For example, your fingerprints are scarce, but that doesn't mean they have any exchange value.
https://en.bitcoin.it/wiki/FAQ#Economy
For mining, the concept is somewhat simple. Regular people with computers mine blocks. Blocks are what contain every bitcoin transaction. To confirm a transaction, when you send or receive money, the info gets put in a block. After 6 or so blocks, that info will be mined out, and your transaction will be confirmed, so the money that got sent to you will be yours, or the money that got sent to somebody else, he/she will receive. The way its setup is to where people don't mine for nothing, otherwise people wouldn't mine. Instead, you get a reward. It was 50 coins originally, now its 25. It halves every couple years. This serves two purposes. One, to give you a purpose to mine. Another, to get more bitcoins in circulation.
Bitcoin mining has been warped and a lot of people think of it as a way to make money. But its much more than that.
