IN PLAIN ENGLISH:
Smart contracts enable services, products or information to be bought and sold in a fair, honest and automated way without the need for a trusted third party to enforce the contract.
The details:
Smart contracts are a brilliant creation of the Ethereum blockchain. It is a great example of the powerful things that can be done with blockchain technology, besides just be used as a ledger for cryptocurrency.
Let's say you want to have a logo designed for your company. With a smart contract, you can specify all the details of what is required in order for a job to be considered successfully completed, and payment to be issued.
Let's say the finished file needs to be of specific dimensions, color space and file type. You set the requirements and price you will pay (in ETH cryptocurrency), and then your part is done.
A graphic designer looking for jobs finds your smart contract which outlines the project requirements. She does the work, submits the file, and the smart contract automatically verifies that the technical requirements set out in the contract have been met. If so, it automatically issues the pre-determined payment to the designer. If the requirements have not been met, payment is not issued.