I vaguely understand how it's supposed to work for contracts. The idea is that when you create a contract you create certain terms for money and goods/services to be exchanged. The blockchain acts as a neutral and theoretically anonymous entity capable of taking action when conditions are met. Say you form a contract to sell widgets to ACME. You and ACME agree on the terms, and they put so much money into trusteeship of the contract, and the contract delivers some or all of the money directly to the account of your choice, upon delivery of the widgets, confirmation of shipping, etc. Other applications include smart properties that change full or partial ownership based on whose money is placed in trusteeship of the blockchain.
I may be completely wrong but that's how it was explained to me.