the term 'protein synthesis' is a common marketing word used by supplement companies.
however, protein synthesis is a natural process your body does regardless of supplementation. plain old food enhances to protein synthesis far more than any supplement.
to manufacture proteins, cells follow a very systematic procedure that first transcribes DNA into mRNA and then translates the mRNA into chains of amino acids.
these amino acids are necessary for many biological process in the body including structural support of cells (building muscle falls into this category).
supplementation is popular because you can provide additional help to increase or make it easier for your body to synthesize protein. whey protein comes to mind.