From Wikipedia:
A smart contract is a computer protocol intended to digitally facilitate, verify, or enforce the negotiation or performance of a contract. Smart contracts allow the performance of credible transactions without third parties. These transactions are trackable and irreversible. Smart contracts were first proposed by Nick Szabo, who coined the term, in 1994.
Proponents of smart contracts claim that many kinds of contractual clauses may be made partially or fully self-executing, self-enforcing, or both. The aim of smart contracts is to provide security that is superior to traditional contract law and to reduce other transaction costs associated with contracting. Various cryptocurrencies have implemented types of smart contracts.
This video explains what smart contracts are and what do they have to do with blockchains and cryptocurrencies.
In this video, the trainer Kevin Healy gives an introduction to smart contracts in ethereum. First Kevin explains what accounts are in a simpler currency only blockchain. Then he shows how ethereum introduces a second type of account: a code controlled account (aka smart contract) and ten he gives examples of how you can use smart contracts.
