A smart contract is a programmed contract whose appointments are recorded in computer language on the blockchain. The contract is automatically executed without the need for (trust in) an intermediary. These appointments can always be viewed, but cannot possibly be modified.
A smart contract is anything but a paper contract under which you sign with a pen, as we are used to. The smart contract contains all the information of the contract: the persons between whom it is valid, when the contract should be executed, when the agreements have been made, ...