Polkadot smart contracts are self-executing contracts that have a set of predetermined rules and conditions. These smart contracts are generally written in Rust, the programming language used by the Substrate framework. The Substrate framework is custom-built to develop parachains in the Polkadot ecosystem. Smart contracts on Polkadot allow developers to create dApps (decentralized applications) and execute programmable logic. They also facilitate completing different functions, including token transfers, governance mechanisms, and decentralized finance (DeFi) protocols. 

Polkadot smart contracts can interact with the Polkadot ecosystem and leverage its shared security and interoperability. However, Polkadot’s Relay Chain does not support smart contracts. Instead, parachains in the Polkadot ecosystem come with smart contract support.