The very basic idea is that you can create intelligent, multivariate contracts that are secured by a blockchain architecture. The basic idea being that if you want to buy my widgets, we can make an intelligent contract that sets the rate of exchange between widgets and currency. This contract acts as a perfectly neutral third party that holds your money in trust until you confirm that you have received my widgets, upon which point it transfers it into an account of my choosing. You could engineer different rates of exchange at different bulk amounts, or payment schedules that vary based on whatever you want. You could make a competitive contract that automatically contracts with whomever's bid is the best based on your parameters, or whomever meets a certain set of conditions first.

Other applications include smart properties that change full or partial ownership based on whose money is placed in trusteeship of the blockchain. Like, you put $2000 into an account online, you walk to a car you've never driven before, wave your phone over the door, when you park the blockchain deducts the cost of the gas/insurance/whatever from your deposit. When you're done with the car you take the remainder out.