Here are the fundamentals if you want them:
1. You can really own bitcoins while you never really own dollars or gold. You can move them, store them, shuffle around, for a very small price and always have an ultimate control of where they go. http://blog.oleganza.com/post/67362431718/you-can-own-bitcoi...
2. Blockchain allows registering all sorts of proofs for many different kinds of protocols. It can replace DNS+SSL in a single solution where you really own your username like you own a bitcoin.
3. Bitcoin allows to program complex contracts to be enforced by the whole network thus reducing need for vaults, audits, lawers, laws, police force etc. If I lock up my savings in a time-locked transaction for 10 years which needs any 3 signatures out of 5 of my friends and relatives to redeem, there's nothing in the whole planet that can steal this money from me. Or, I can make a bilateral 200% deposit with a total stranger and trade under whatever rules we agreed upon without having reputation systems: http://blog.oleganza.com/post/58240549599/contracts-without-...
There's a lot more to it. It's not just a "payment network".