Kid-friendly explanation: if you move electrons near a magnet, the electons get a push. If the electrons are free to move, the push gets them moving and moving electrons is electricity.
Easy source of electrons that can move: a wire. Metal has lots of electrons that are pretty easy to move around. If you hold a wire and wave it past a magnet you get electricity in the wire. Give a kid a coat hanger and a bar magnet and have them go to town, they’re making electricity.
A conventional power generator is just a way of moving a *lot* of wire past a *lot* of magnets, but the physics is exactly the same.
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