Perhaps the best way to describe Bitcoin mining to the layman would be to say that it is somewhat like a cross between the California Gold Rush and the lottery. No one is given Bitcoins per se. You've got to earn them. At the same time, you need a little luck. No one can precisely define how long it will take to successfully mine a Bitcoin. While your chances should become better with the more hashes you can generate, there is not always a direct correlation between the amount of work you put in and the rate of success you are going to have.
Bitcoins are a new currency, and they work on a peer-to-peer system, so there is inherent value in their relative scarcity, as well as its independence of a "central authority."
Bitcoin mining becomes more difficult over time, in order to facilitate limitation on the supply. It is referred to as a "high performance computing problem" and thus is best solved with hardware that is specifically built for that purpose. In order to mine Bitcoins, you have to "solve a block," and that gets harder as the network of miners grows. Proof of work must be shown for anything to be valid. It is a very competitive endeavor. To help improve the odds for success, miners often form pools, where resources are combined and any yield from the effort is divided.
Aside from uncovering Bitcoins, which brings its own reward, miners have another incentive; namely, the fees they can collect for transactions on the part of users. So they are motivated to include transactions in their block. This becomes a more important factor as the difficulty in creating new Bitcoins increases.
It's cutting edge, and a ground floor opportunity. It's clearly no wonder why so many people are excited by Bitcoins!