When you sing, or speak, you unconsciously exercise extremely fine control over many different muscles. Everyone can do this. If you want to get some formal training, you can learn to be aware of certain muscles and how to control them even better.
I studied singing in college for four years. Singing is indeed an "athletic" activity, in that it involves toning and strengthening muscles, and developing stamina in using them (as well as learning how not to fatigue or damage those muscles). Knowing a bit about physiology plays a certain role, but the larger role is in singing and listening carefully to the sounds you are producing. If you are producing better and better sounds, with more and more ability to control those sounds, and to develop stamina and avoid fatigue, then you are improving your muscle strength.
The key to all this is to start out by taking regular lessons from a good professional voice teacher who can teach you how to improve your singing, and give you valuable feedback on correcting bad habits and building good habits. After you have studied for some time, you will learn how to do it by yourself, and be aware of whether you are singing at your best, or not.
Doing a certain set of warm-up singing exercises every day (you and your voice teacher will arrive at a regimen that works for you) is important to keeping your voice in its best condition. If you don't sing every day according to a certain regimen, you will find that it will take you several days to get your voice back into proper shape again. This is very much like daily training for athletes.
Singing well requires many different muscles. The diaphragm muscle in your abdomen is the largest and strongest muscle in the body. It is what enables you to breathe in and out with your lungs. There are also other "costal" muscles that are involved in taking a deep breath and controlling how your air is expelled while singing or speaking. Then there are the many small muscles in your larynx and throughout your mouth and sinuses that you learn to control in minute amounts to produce all the effects of speaking and singing. If you are untrained, you don't think much about these muscles at all. If you get some voice lessons, you learn to be aware of where these muscles are and how to manipulate them.
At first it is quite daunting to learn that in order to sing well, you have to be conscious of all of these different muscles and how to position them. But with continued practice, this becomes second nature.