Like many ideas in the blockchain industry, a general confusion shrouds so called 'smart contracts'.
A new technology made possible by public blockchains, smart contracts are difficult to understand because the term partly confuses the core interaction described.
How smart contracts work
It’s worth noting that bitcoin was the first to support basic smart contracts in the sense that the network can transfer value from one person to another. The network of nodes will only validate transactions if certain conditions are met.
But, bitcoin is limited to the currency use case.
By contrast, ethereum replaces bitcoin's more restrictive language (a scripting language of a hundred or so scripts) and replaces it with a language that allows developers to write their own programs.