It's well established that branched-chain amino acids (particularly leucine) stimulate protein synthesis, and might do so to a greater extent than a normal protein on its own. BCAAs also increase synthesis of the cellular machinery responsible for carrying out the process of protein synthesis. Thus, BCAAs not only increase the rate of protein synthesis, but they also increase the cell's capacity for protein synthesis! Yep, you read that right.
BCAAs also work in your favor by reducing the rate of protein breakdown.