What makes your muscles look bigger when you flex them, when you "make a muscle" with your biceps, for example?
Muscle cells contain long strands of protein lying next to each other. When you want your muscles to move, your brain signals your nerves to stimulate them. A chemical reaction in your muscles follows, causing the long strands of protein to slide toward and over each other, shortening the length of your muscle cells. When you "make a muscle" and you see your muscle bunch up and bulge, you are actually watching it shorten as the protein strands slide over each other.
When you do challenging muscle-building exercises on a regular basis, the bundles of protein strands inside your muscle cells grow bigger. And that's how your muscles get bigger. It's just that simple.