A program that runs exactly as written
A smart contract is a program that lives on the Ethereum blockchain and runs on the EVM. There's nothing magical about the word 'contract' here, it isn't a legal document, it's code, the same way a function in any programming language is code. What makes it different from a normal app on your phone is where it runs and who controls it: instead of living on a company's server that they can edit, restart, or shut down at will, a smart contract's code is stored on the blockchain itself and executed by the same distributed network of nodes that secures the rest of Ethereum.
Because every node runs the same code and checks the same result, a smart contract behaves predictably. If you call a function on a contract, it does exactly what its code says, no more and no less. There's no customer support agent who can override the outcome, and no hidden business logic running somewhere you can't see. That predictability is the whole point, it's what lets strangers who don't trust each other agree to interact through a contract instead of through an institution.