What does protein synthesis have to do with genetics/ heredity?

Proteins are polymers of amino acids and their structure determines function. So the determinant of structure is the amino acid sequence which is coded in the DNA, or the genes. So you get the structure of your proteins from your parents. And they got it from their parents. If the structure of your proteins differ from the structure of someone else's protein, either you or the other person may have an evolutionary advantage and when you p your DNA to your offspring, they may have an advantage over other people's offspring who have a slightly different DNA sequence.