If you really are serious, here's the 101.
Strength largely comes from muscles contracting. Muscles are made up of long fibers, and when you see a muscle contracting what is happening is the fibers themselves are contracting (getting shorter). One of the main things that determines how much power muscle fibers produce when they contract is their thickness. When you see people with big muscles, that is part of what you are seeing- thick muscle fibres.
But there are lots of other things that can make someone strong or less strong, but you can't see them (they won't be bigger or smaller). E.g. it matters a lot how many of your muscle fibers you can contract. If you never lifted heavy weights you might only be able to contract half of them at a time for example. As you train more you get better at contracting more of them. (This is called "neural efficiency"). It also matters that you can contract them all at the same time- if they don't quite fire at the same time you won't be as strong. It matters how often your brain can send the signal to the fibers to contract (rate coding). It also matters how the tendon that connects the muscle to the bone is attached to the bone. If the connection is closer to the joint, you will be stronger. Technique matters too, for compound lifts like the squat. If you do the lift in an efficient way you can lift a lot more.
There are actually a *lot* of other things that can make you stronger or weaker, that are not related to size/muscle size.