Smart contracts are simply computer programs running on a blockchain that execute when a user (or another contract) interacts with them. A combination of smart contracts can be bundled together into dApps or decentralised apps.
Once a smart contract is uploaded to Ethereum, it is available for the duration of Ethereum's existence unless permanently destroyed by specifically outlined parties with explicit permission. Typically, these permissions are afforded to the developers who created the contract, and tend to have additional requirements, such as multiple parties needing to take action in order to destroy a contract.
With this setup, smart contracts are almost always available for usage and tend to not favour any one user over another.
Common instances of smart contracts include:
Lending applications
Decentralised exchanges
Insurance
Games
Social Media