How to explain a startup?

You shouldn't, at least not initially. Your objective should be to say in concrete terms, the one core thing that your startup does.

So if your startups is to build control towers, then your startup explanation is, "We land planes."

Most people need a conceptual trunk to hang the details of your startup on. If you don't establish that in the very beginning, you're going to lose them very quickly.

What is the objective of explaining to someone? Is it to validate your idea/product/service? Are you seeking funding with potential investors? Or just to explain to someone what do you do?

I can think in a different answer for each case :)