I honestly do not get Bitcoin. Whenever I read about it I feel old and stupid.
There are a lot of moving parts, and there are several distinct roles one might play in bitcoin. You hear about mining it as a way to make money, sending bit coins to people, and bitcoin exchanges, and it all becomes a big muddled mess.
For the consumer, bitcoin is an agreed upon currency, just like the dollar, yen, or any other currency. It fluctuates in value over time, but it'd just a form of money. The value is market driven, and the is no real central authority or backer. It isn't backed by gold, or a country, or anything else. The value is entirely, completely, market driven.
As such the US, for instance, can't strengthen or weaken it merely by printing more bit coins like they can with the US dollar.
Further it's designed so that transactions cannot be tracked. At all. I give you a number, you "send" bit coins to that number, and I get them. It's not an account number, and can't be tied to me except by my revealing it to someone. Further, I can generate an infinite number of these, so I could use a different number for each transaction, completely hiding who is getting the money you send. You can't find me with that number. When you send bit coins, you actually insert a little piece of information that encrypted with that number into the global bitcoin data stream. Eventually my "wallet" sees that encrypted piece of information, and can retrieve the bitcoin, while everyone sees the block of info, there's no way for them to know who sent it, or who received it. Further, they can't receive the coin themselves because of the encryption used via my number. Only my wallet (which gave me the number) can decrypt the message and retrieve the data that says, "here's some bitcoin". Inserting a transaction into the global data stream comes at a small cost, a transaction fee. This is a sort of payment to make sure the data in your transaction gets processed and added to the global data stream.
And that's it, for the consumer facing side. You don't really need to know anything else. You can get bit coins by sending someone else money at their exchange rate, and they'll give you bit coins they already have, or reverse it and give them bitcoins for cash. The are a number of exchanges people have set up to make this easier.
Since one primary goal was not to have a central authority or transaction processor, the inventor of the scheme decided to spread that work across everyone that wanted to participate. Each transaction requires additional work in the way of very difficult decryption before it can then be pulled back out of the data stream. So before you get your money, the network has to solve a series of very difficult math problems and searches. Once that's done, you'll get your money.
This process is called mining. Currently when you mine there are two things that happen, first is that new bitcoins are created. These become new currency and are given to the transaction processor, ie miner, that solves the problem first. The second thing that happens it's that a block of transactions are processed into a format where they can be retrieved.
Each block produced reduces the bitcoin creation, and eventually all the bitcoins there will ever be will have been created. After that the transaction fees are the only thing the miners will get for all this work.
The work is hard enough that a high end computer with a high end video card can solve the problem in a week or two. It's not very fast, so people work on these problems in parallel. By giving a hundred computers the same problem, but telling each one to look at only a small division of the possible problem space, the time to solve is much faster. Now they have custom microchips doing this work, and even then it takes minutes before a new block is solved.
So you might not get your money for minutes, or even hours, after it was sent. Blocks are solved sequentially, miners can't skip ahead, and only the fastest miner actually wins the reward. However the problems are designed so that finding the solution is actually random time, so as long as you keep mining at the same speed as everyone else, you'll get rewards as often as everyone else.
It's no longer something that mere mortals can hope to do and win, though. The customs chips have long since surpassed the capability of even the best alternatives.
I don't know if this clears things up, or just confuses you further. It's a fifty thousand foot overview, and for the sake of understanding I've simplified things. If you dig into it, the transaction processing model is a bit different than I've described, but this suffices to portray what is happening inside the system.
Note that if one person or group owns more than fifty percent of the bitcoins, they can completely change the currency at the code level. It's unlikely to ever happen, but the currency is essentially democratic, and thus fallible by design.
