What is an atom and why is it so small?

Pick up anything at all — a spoon, a strawberry, your own thumb. Now imagine chopping it in half, then half again, then half again, getting smaller and smaller until you can't chop anymore. The tiniest piece you'd reach is an atom: the basic building block that everything is made of. So what exactly is it, and why is it so impossibly small?
An atom is mostly empty space with a tiny clump in the middle. That clump is called the nucleus, and it's packed with two kinds of particles: protons and neutrons. Buzzing around the nucleus, far out at the edges, are even tinier particles called electrons. That's it. That's the whole recipe for everything you've ever touched.
