What is a smart contract, and what does it enable?
A smart contract is a set of instructions deployed on a blockchain that executes automatically and cannot be altered once deployed, letting parties make self-enforcing agreements without a trusted middleman.
Think of an ordinary contract — a set of terms between parties — but written in code and deployed onto a decentralized blockchain instead of signed on paper. Once deployed it has three defining traits: it executes automatically when its conditions are met, it is immutable (nobody, not even its author, can change the terms afterward), and it is transparent (everyone can read exactly what it will do). Because a group of decentralized nodes runs it rather than any one party, no single person can flip a switch to break the deal in their favour. This is what "trust-minimized agreements" or "unbreakable promises" means: instead of trusting a company to keep its word, you can read the code and know the outcome is guaranteed every time. Nick Szabo proposed the idea in the 1990s; Ethereum was the first blockchain to run arbitrary smart-contract code, whereas Bitcoin's scripting is deliberately limited.
Go deeper:
Smart contract — Wikipedia — history from Nick Szabo's idea to on-chain programs.
Introduction to smart contracts — ethereum.org — what a deployed contract is and how it runs on-chain.