Strength is not only the physical capacity to generate force but also a skill, your body needs to learn how to apply force correctly during a specific movement. The Neural adaptions to strength training involve increases in the number of motor units firing as well as the ability to increase the frequency of impulses know as rate coding this makes up intramuscular coordination. It also improves Intermuscular coordination which is the body's ability correctly orchestrate the muscles of the kinetic chain to make the movement more efficient.
The ability to increase motor unit activation begins in the motor cortex with the intent to produce maximum levels of force and power this is why we always stress that submaximal loads must be moved with maximal intention. Maximal force production requires not only the recruitment of the maximum number of available motor units but also that these units fire and very high rates. At this stage, I wasn't too sure how far into the science of how this all works without sending you all to sleep. I'm more than happy to expand on this in more depth if you guys want to know more but my main take-home point is that strength isn't just a product of muscular size but of one's ability to recruit the maximum number of motor units and contract muscle in the correct sequences. Because of this, we should view strength as a skill. Yes a larger muscle does have a higher cross-sectional area, and at some point, specific hypertrophy will be needed to increase force production but simply just having a large muscle mass doesn't guarantee maximal strength.
This post isn't intended to take a stab at bodybuilding style training as this certainly has its place with a training program especially when it comes to achieving muscular balance throughout the body and is a very effective way to bring up a weak and lagging muscle group. But when it comes to improving strength displayed in movement focus on training the actual movements and frequently, so you're able to work on the intra and intermuscular coordination of the exercises.
The majority of intramuscular coordination gains involves using loads over 80% (of 1RM) while the majority of intermuscular coordination gains include using loads under 80% (of 1RM). Looking at the chart below it becomes clear that the majority of strength training should take place in the 70-90% range to elicit the maximum gains in Intra and Intermuscular coordination with loads of 90% or higher only being a small percentage of the yearly training intensity.