The are not really empty. But the nucleus of atoms has a lot of matter packed into a small area.

Atoms can be best understood as quantum mechanical objects, which basically means they are waves, kind of like sound waves in air, but they are standing waves, like a vibrating string. The nucleus is is a really intense wave concentrated in a very small area, kind of like the spike of water that leaps up when you drove a small rock into water, whereas the electrons form much smaller waves distributed over a larger area, more like the ripples that radiate out.

The thing about those electron waves is that they like to be pretty close, but not overlap too much, and that’s what allows molecules to form and what keeps molecules from collapsing into a single super-atom, and also what keeps substances made out of molecules from collapsing. If you try to get an atom to pass through another one, those waves will bump up against each other and prevent it from happening, unless they’re moving really fast.

So in short, it’s not that atoms are empty, but that atomic nuclei are really dense.