Scientifically speaking, protein synthesis is the process by which cells build protein molecules using DNA, RNA, and enzymes. Practically speaking, it's a process during which your body uses the amino acids found in protein to build new muscle.
Over the course of a day, your body fluctuates between two processes: muscle building, also known as protein synthesis or "anabolism," and muscle breakdown, also known as "catabolism."
After taking a protein supplement, there is a short period during which you have elevated amounts of amino acids in your blood. This period, known as hyperaminoacidemia, stimulates greater than resting amounts of muscle protein synthesis.
Hard training is catabolic, in that you inflict damage on your muscles and break them down. But after training, your body almost immediately becomes anabolic and starts healing up that damage. Having a pre-workout or post-workout protein shake, or a solid meal with adequate carbs and protein around training, helps kick-start this process. The amino acid leucine, which is plentiful in protein powders and protein-rich foods, is fundamental here.
In "Mass Class Nutrition: The Fundamentals of Eating for Growth," Jacob Wilson, Ph.D., outlines a simple plan to get the most protein synthesis possible over the course of a day.
"To maximize the muscle-building response, you need about 3 grams of leucine per serving, and that's actually what the 30-40 grams of protein in your meals gives you."