A normal contract is an agreement between two or more parties that binds them to something in the future. Alice may pay Bob some money in return for use of Bob’s house (aka rent). Charlie may agree to repair any damage to Denise’s car in the future in return for a monthly payment (aka car insurance).
The key feature of a smart contract is that it has trustless execution.
That is, you don’t need to rely on a third party to execute various conditions. Instead of relying on the other party to make good on their word or even worse, relying on lawyers and the legal system to remedy things should something go wrong, a smart contract executes what’s supposed to happen timely and objectively.
Smart Contracts are Really Hard

Because of a lot of centralized marketing from Ethereum, there’s a mistaken belief that Smart Contracts only exist in Ethereum.