Some further context:
Computers all over the world are competing to extend the block chain by solving a problem involving cryptographic hashes. The reward for solving the problem is that a wallet controlled by the machine that does it can claim a Bitcoin reward. The reward is currently, I believe, 25btc --- but it's scheduled to drop over time; eventually to zero, at which point, miners will have to be compensated by claiming transaction fees.
The upshot is that Bitcoin has a system for maintaining a single, global log which is consistent across all connected Bitcoin clients. And while Bitcoin itself uses this as a transaction ledger, there are plenty of other things you might want to use this construct for once you have it. Namecoin, for instance, uses a Bitcoin-like block chain to manage a DNS-like naming scheme.
(There are some weaknesses to the design: most notably, if a single party has more than half the mining compute capacity, they're able to pull off all sorts of chicanery against the community as a whole...)