I do drug discovery for a living, so my own field doesn't provide as many elegant explanations as I'd like—not yet, anyway. Physics and math, though, are a collection of jewels, since mathematics can't seem to help being the material the world is made from.
And while there are explanations whose depth and power make you have to sit down for a while once you take them in, many of these require some mathematical scaffolding before you can get a good view. But one of my favorites can be explained to children. I know that because I've told it to my own children, and because it's one that I worked out in my head while I was still a child myself.
Watching the Apollo program unfold on television, I kept hearing about "zero gee", a term that still makes people think (wrongly) that someone in orbit has somehow escaped Earth's gravity. But explain it this way: imagine throwing a rock across a field. You can picture the big arc it makes as it goes off into the distance—gravity's rainbow, in the phrase. To throw it farther, you have to throw it higher, and harder, making a bigger arc that takes it out more into the distance.
Now imagine really getting some air, using a catapult, a cannon, or whatever you like. The rock arcs out higher and faster, and lands farther and farther away, farther than you can see in the distance: across your town, across your country, across the nearest ocean. Eventually, you launch it so high, so powerfully that it falls over the distant curving edge of the earth itself. Instead of coming down, it literally misses the ground and falls out over in a huge whooshing loop around the planet. You have launched your rock into orbit, and instead of talking about zero gravity, you should call it by a better name: free fall.
And this makes the rest of it easier to picture: why rockets go off to the side as they take payloads to orbit, how lower orbits are faster and higher ones slower, how they can eventually spiral in and decay, and why "escape velocity" means exactly what it says. When I think of space and orbital mechanics, I see myself as a boy again, throwing rocks across a field into the Arkansas sky and dreaming about what would happen if one never came down.