The main structure in the cell responsible for protein synthesis is the ribosome. Ribosomes are cellular organelles that facilitate the translation of messenger RNA (mRNA) into polypeptide chains, which then fold into functional proteins. They can be found floating freely in the cytoplasm or attached to the endoplasmic reticulum, known as rough ER, indicating their crucial role in synthesizing proteins for both intracellular and extracellular functions.