"Programmable money" is one shorthand example for smart contracts. As a simple example, you could create a payroll smart contract that pays a fixed amount of coins/tokens/whatever at a certain time each month to a given ERC20 compliant address. You can contrast this with Bitcoin, whose two main functions are securely storing and sending bitcoin (limited by design).

For a more in-depth answer regard smart contracts, here is an article by Vinay Gupta where he sets the context for Ethereum, smart contracts and blockchain against the existing way of organising and sharing data (SQL, the web, how organisations share data, protocols, and more):

https://medium.com/humanizing-the-singularity/by-the-end-of-...