There are some different opinions and ideas about this subject. The truth is that we do not fully understand how muscle develops. Think of your muscles as an elastic band for a second. When we stretch out the muscles they become longer, just like with an elastic band. When we contract muscles they become shorter. The same would happen if you relax the elastic band from the stretching position.
One of the theories of building muscle is that working out (such as weight lifting or calisthenics) will make very small tears in the muscles (so-called micro-tears). Your muscles get "damaged" from working out is what is believed. When we rest, eat adequately and sleep we will rebuild those damaged muscles. Our body is smart and to avoid more damage it will make the muscles stronger and bigger to ensure it will not get these micro-tears again.
This will make our muscles grow and is called Hypertrophy.
Another theory, which is the one I believe in most, is the one that tells us that working out imprints memories in our brains. When you practise tennis and try to learn the backhand volley, your brain and body work together. Our brain sends signals and receives signals to and from our muscles to form a certain movement. At first the technique seems very difficult and we need to think a lot about it. But once we train more our body will be able to perform the movement better. It will take less effort to perfectly demonstrate the backhand volley technique, because our body adapted.
The same thing happens with growth of muscle mass. When you lift 10 kg for 5 repetitions of a given exercise (say dumbbell curl) you will probably feel it is quite heavy. The next morning you will definitely feel it was heavy, because you could feel pretty sore. Our body, meanwhile, has learned that lifting 10 kg for 5 repetitions is quite difficult and actually too difficult. So to solve this problem it will build stronger and bigger muscle to carry out the task.
Think of it this way: You just bought yourself a bookcase and had put it together after 4 devastating hours of reading an illogical building plan. Anyway, you put the books on the shelf and since you are such a smart-ass reading all these big, thick books, the shelf collapses. The load was too heavy. I just told you that you were a smart guy (just play along for now) and add another shelf right under the one that just collapsed.
Now reinforced, your shelf can hold up all your books. Pay check just came in and you decide to buy a book about biomechanics. It contains 2000 pages and weighs 4 kg. You put it on the shelf and you hear something snap. The increased load was too much for the shelf and so you have to put a third shelf under the first two (I know, unrealistic story, but still).
I think, and most desperately hope, you understand these two theories. Your muscles, just like the rest of your body, are made up out of cells. Muscle cells in this case. When we are speaking about hypertrophy, we think of the cells growing in volume. You will not necessarily get more muscle cells, but they become bigger. In the articles Growth and Nutrition and Stimulating Growth you can read more practical information on how to get more muscular.
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