The answer is motor unit recruitment and refined motor patterns.
Your muscles are controlled by the nerves in your brain. Each nerve is connected to several individual muscle fibers, so just one neuron is needed to get several muscle fibers contract at once. However not all of the motor units contract at once. So you could flex your bicep, but maybe only half of the muscle fibers would be activated. The stronger the contraction, the more motor units that are recruited to produce a stronger force. This is called motor recruitment.
Imagine that you're trying to push your car down the street, but you're having a bit of trouble. You have seven friends that are just standing there with nothing to do, so you ask them to help you push the car down the street. You and each of your friends could be considered a separate motor unit.
So imagine you ask your friends to help push the car, but only five of them decide to help. This happens not because your friends (motor units) are lazy, but because they haven't been trained to work together yet.
Your brain has to be conditioned to activate all of your motor units to work together to produce a stronger contraction. This is known as motor unit recruitment. Motor unit recruitment is responsible for most of the strength gains made by your muscles in the early stages of strength training.
In other words, you can have a lot of friends (motor units) with big muscles, but if they don't know how to work together at once as a coordinated unit, you'll never be as strong as a guy that has less friends, but that work well together.
Even when you try flex your muscle as hard as you can, not all of the motor units will be activated; you need to practice strength training. Strength training is all about refining your motor patterns. You can think of it as teaching all of your friends how to push the car down the street as a coordinated unit. The more you lift, the better your brain gets at activating more and more motor units. So when you get stronger from weight lifting, it isn't just because you're getting bigger muscles, it's because you're activating a higher percentage of your muscle fibers.
So if you want to push the car down the street without getting more friends (bigger muscles), your friends have to practice pushing the car at the same time to work together all at once. This means that when you train, you have to activate as many muscle fibers as possible. Your brain needs to practice activating the motor units together, otherwise, it will never do it when you need it.
Your training should consist of activities that activate as many muscle fibers as possible. This means strength training with a heavy weight in an explosive manner. Moving a heavy weight as fast as you can will get all of your motor units to chip in at once. Power lifting and plyometric exercises are great at getting a maximal contractions. Lifting lighter weights with higher reps and less speed will get you more muscle, but it won't necessarily teach your brain to activate all of your motor units.
As long as your muscles are contracting at full speed or full force, you'll be activating as many motor units as possible. Do that repeatedly, and you'll get better at it.