This is not a perfect analogy, but to give you a simplistic analogy of what Bitcoin mining is like.

Take something that we're all familiar with--lottery tickets. A lottery ticket has a series of numbers on it. Imagine a Bitcoin as a digital lottery ticket with a unique set of numbers on it. According to the Bitcoin rules, only one lottery ticket can exist with that particular set of numbers.

When you "mine" Bitcoins, you're essentially just selecting a new set of numbers for a new lottery ticket, but before that ticket is considered valid by everyone else, the Bitcoin protocol requires that you have to put in some "work". Around the world, there are public lists of all valid Bitcoins and information about them, like a history of transactions, so it's like every lottery ticket ever issued is listed and publicly accessible. Say the work, or mining, involved multiplying all the numbers on every lottery ticket in existence. Obviously, as the number of lottery tickets expands, so does the amount of processing power required to finish the necessary "work". Once you have finished the work, your new lottery number is then distributed to all the servers and anyone who tries to claim that number in the future will be rejected.

Very, very simple analogy.

In the beginning, it didn't take much work to generate a Bitcoin because not many existed but now the work is beyond the horsepower of typical home PC's. That's why there are companies selling specialized hardware that are optimized for blazing through these Bitcoin calculations. There are whole data centers out there devoted solely to Bitcoin mining. As the number of Bitcoins increases, the work requirement acts as a feedback mechanism that slows the growth of the Bitcoin supply. There is also a hard maximum number of 21 million Bitcoins that can ever exist but we're still a long ways from reaching that limit.

When you "spend" a Bitcoin, you're just transferring ownership of that lottery ticket number from you to another person in a way that all these public servers are notified. So, you can't just reuse the same lottery ticket number over and over because the public registries have recorded that you don't "own" that lottery ticket anymore. It's like buying or selling a house. When you buy a house, you do a title search to make sure the seller owns the house free and clear and then you register the transaction with the appropriate government agency in your name.

You can even split one Bitcoin into fractional ones. It's mostly a bookkeeping thing with the public servers, so you can "spend" a tenth of a Bitcoin and still have nine-tenths of it remaining in your possession.

In terms of the value of a Bitcoin, think of them like stocks. They are constantly being bought and sold on exchanges and the prices varies as the supply or demand varies. The price swings can be very quick and dramatic, which scares many people but you can also make a killing in a short time if you get the timing right.