Why are blockchains well suited to smart contracts, and what did Ethereum add over Bitcoin here?

A blockchain is a distributed state machine with no trusted third party, which is exactly what a self-enforcing contract needs; Bitcoin allows only a limited scripting set, while Ethereum was first to run arbitrary code on-chain.

A smart contract is a digital contract that is self-enforcing — or makes breaking it prohibitively expensive. Because a blockchain executes agreed code and updates shared state without anyone in charge, it can enforce such contracts trustlessly, simplifying protocols between parties who don't fully trust each other. Bitcoin supports a restricted set of contract-like scripts; Ethereum was the first blockchain to allow arbitrary code execution on-chain, enabling any kind of smart contract. Either a permissionless or permissioned chain can host them, depending on requirements. Caveat from the paper: because practical smart contracts are still new, how far they're legally binding remains unsettled.

Go deeper:

• Smart contract (Wikipedia) — self-executing on-chain code, and Bitcoin's Turing-incomplete script versus Ethereum's Turing-complete language.