I would like to explain how the Ethereum smart contracts get initiated to run, and what they are, to a non-technical friend. I do not need to explain to them the execution of the contracts and the programming language that makes it programmable. I do not need to explain to them the P2P networking and decentralization. I simply need to explain the mechanism involved prior to executing a contract.
As analogy, think about it as explaining a vending machine. Inserting a coin into a vending machine is the transaction (me sending the money). Deciding whether it is the right coin (or the right amount) is the work the miners do. Selecting the product from a vending machine is the execution of the smart contract. What I need to explain to them is the part where the machine decides whether it is the right coin or the right amount of coins, just before executing the order I made.
A good answer that was already given is here: At which point the smart contracts get executed?
However, what the answer lacks is explanation of the architecture and logistics.
Lets just say that I need something that can be put into an illustrated flow-chart, and that they will understand it when written in such a manner.