How Muscles Grow

Your muscles grow when they recover after heavy stress that you put on them in the gym. 
Your body 'thinks' that you were running for your life from a lion and nearly escaped, and it builds some extra muscle to make sure that you outrun that lion next time he finds you! 
The same story in other words: when you stress your muscle to the limit, it develops micro-injury. 
When it repairs the damage, having enough time and material, it 'overdoes' a little, to prevent you from having that 'micro-injury' in the future.

To put it short, if you want your muscle grow, you should give it as much stress as possible in the gym, then you should provide it with everything it needs to recover and grow, which is time and food. 
Do not stress the same muscle every day - it will not have enough time to recover and grow.

When muscles undergo intense exercise, as from a resistance training bout, there is trauma to the muscle fibers that is referred to as muscle injury or damage in scientific investigations.
This disruption to muscle cell organelles activates satellite cells, which are located on the outside of the muscle fibers between the basal lamina (basement membrane) and the plasma membrane (sarcolemma) of muscles fibers to proliferate to the injury site.
In essence, a biological effort to repair or replace damaged muscle fibers begins with the satellite cells fusing together and to the muscles fibers, often leading to increases in muscle fiber cross-sectional area or hypertrophy.
The satellite cells have only one nucleus and can replicate by dividing.
As the satellite cells multiply, some remain as organelles on the muscle fiber where as the majority differentiate (the process cells undergo as they mature into normal cells) and fuse to muscle fibers to form new muscle protein stands (or myofibrils) and/or repair damaged fibers.
Thus, the muscle cells’ myofibrils will increase in thickness and number.
After fusion with the muscle fiber, some satellite cells serve as a source of new nuclei to supplement the growing muscle fiber.
With these additional nuclei, the muscle fiber can synthesize more proteins and create more contractile myofilaments, known as actin and myosin, in skeletal muscle cells.
It is interesting to note that high numbers of satellite cells are found associated within slow-twitch muscle fibers as compared to fast-twitch muscle fibers within the same muscle, as they are regularly going through cell maintenance repair from daily activities.
Resistance training leads to trauma or injury of the cellular proteins in muscle. 
This prompts cell-signaling messages to activate satellite cells to begin a cascade of events leading to muscle repair and growth.
Several growth factors are involved that regulate the mechanisms of change in protein number and size within the muscle. 
The adaptation of muscle to the overload stress of resistance exercise begins immediately after each exercise bout, but often takes weeks or months for it to physically manifest itself. 
The most adaptable tissue in the human body is skeletal muscle, and it is remarkably remodeled after continuous, and carefully designed, resistance exercise training programs.