Ethereum is attempting to create a complete programming language combined with blockchain based trust for writing legal contracts that self execute. This could be a will or trust that cannot be challenged or changed in court. It could be a lease agreement that activates the ignition on your rental car as long as the payments are current. You could use it to create your own bank, or even your own currency. You could setup complex financial instruments like derivatives, or to simply escrow funds. You could even program a peer to peer poker table, and, as long as the players know how to read the code, they can verify the rules and play together with no "house" in control. Ambitious theoretical concepts such as smart contracts and digital autonomous organizations may now be possible. Imagine if there was a bot online that we could send funds to knowing they would be automatically distributed directly to residents in a disaster area with no human control and no overhead cost.
Ethereum can decentralize contract law, the way that bitcoin is decentralizing currency.