Thanks for starting a thread. I do see you have answered quite well, but I would like to add some points to it.
We all know what a contract is, when ever two or more parties agree to some terms before acting on something, they sign a contract in presence of a third party which reduces any counter party risk. And the trust is maintained among the group. But what if there's a contract which holds by itself and does not need a third party to place it to action. In current scenario, the answer is blockchain. As blockchain is a single source of truth and the data stored is near to immutable once written, unless a hard fork happens :D. So, why not deploy a algorithmic code in blockchain and let it work on its own.
Smart contract is a algorithmic piece of code which gets triggered on meeting certain conditions that may be external(feeds) or internal(via executing functions through transactions), which resides in the blockchain.
Once deployed in the blockchain the contact can not be updated or deleted. It can only be replaced by a new one to which all the participating parties agree.
First introduced in Ethereum blockchain, which is capable of running a smart contract in it's Ethereum Virtual Machine.
Applications: