Great article by Marc Andreessen: Why Bitcoin matters.  Good, simple explanation:

"Bitcoin is an Internet-wide distributed ledger. You buy into the ledger by purchasing one of a fixed number of slots, either with cash or by selling a product and service for Bitcoin. You sell out of the ledger by trading your Bitcoin to someone else who wants to buy into the ledger.",

and good review of the implications:

"The practical consequence of solving this problem is that Bitcoin gives us, for the first time, a way for one Internet user to transfer a unique piece of digital property to another Internet user, such that the transfer is guaranteed to be safe and secure, everyone knows that the transfer has taken place, and nobody can challenge the legitimacy of the transfer. The consequences of this breakthrough are hard to overstate."

Marc is perhaps a bit hyperbolic in the parallels he draws to PCs and the Internet, but he makes a compelling case for Bitcoin's importance.

(graphic taken from John Patrick's blog :)