Smart contracts are the fundamental building blocks of Ethereum applications. They are computer programs stored on the blockchain that allows us to convert traditional contracts into digital parallels. Smart contracts are very logical - following an if this then that structure. This means they behave exactly as programmed and cannot be changed.
One of the most significant benefits smart contracts have over regular contracts is that the outcome is automatically executed when the contract conditions are realized. There is no need to wait for a human to execute the result. In other words: smart contracts remove the need for trust.
A simple metaphor for a smart contract is a vending machine, which works somewhat similarly to a smart contract - specific inputs guarantee predetermined outputs.
The vending machine will only dispense your desired product after all requirements are met. If you don't select a product or insert enough money, the vending machine won't give out your product.
You can learn more about smart contracts on ethereum.org.