It would definitely help if the Ethereum folks could present a real-life example of how this will work.  They are speaking too much in hypothetical and theoretical concepts.  As if trying to be-all and end-all in developing the platform/infrastructure/scripting/etc. for crypto-currency 2.0 when there hasn't been any proof-of-concept that can be shown off.  To me, all their pitches are in the ethereal world.

In the above examples, I think these are conditional orders and not contracts.  A contract is between two entities or people -- i.e. an agreement.  For example, a futures contract for soybeans/oil/gold/etc. traded on exchanges such as CME/CBOE is a standard contract that can be traded.  It's terms are known beforehand because they are standardized -- fixed amount per contract, fixed delivery amount, fixed periodic delivery date, etc.

I believe this is what they mean by contract.  And what they are trying to do is to remove the middle-men (e.g. CME, CBOE) with a decentralized approach.  But I'm not 100% sure because of they give no concrete examples -- i.e. in the intro video.

I suggest they crank out a proof-of-concept example/prototype or at least state the first application they want to implement once a good chunk of Ethereum is completed.  Much easier for folks to wrap their minds around a real example rather than via concepts that seem extremely difficult (in my mind) to integrate.