Myosatellite cells are basically inactive structures that are found in mature muscle cells. Depending on the stimulus, they can develop into different things in the muscle.
As I understand it, they have a couple of functions. They can increase the number of nuclei, create new muscle fiber or spawn off daughter cells. The increase in muscle fiber content is fairly obvious as far as benefits, but the increase in nuclei helps with protein production in long, fused muscle fibers.
Both an increase in muscle fiber and an increase in the nuclei will lend themselves to increased performance. It's been suggested that the initial response to stimulus is to increase the number of nuclei, and if the pattern of stress continues, to then start creating new muscle fibers. While muscle fiber may shrink and disappear with detraining, there are some studies that suggest that the number of nuclei do not diminish with detraining, even past the 90 day mark. This may help explain why someone that has performed at a certain level in the past has an easier time returning to that level. (Which has been termed muscle memory).