When people are young, their bodies produce tissue and cells at a much faster rate, and thus, also repair tissue faster as well. This is why it can be so dangerous to get hurt as an older person, because repairing the damage takes much longer and is much slower.
For serious injury there are several different treatments that can help with repairing the tissue at a faster rate. Resting of course helps quite a bit, as does proper diet and getting the right nutrition. There are also medicinal treatments that can help with muscle repair and healing. The more recent advancements involve stem cells, which can replace tissue and repair muscle at a much faster rate. While stem cell research has been stymied in recent years by a lack of government funding, it’s now receiving significant attention and a lot more research funding.