The function of ribosomes in cells is to synthesize proteins by translating messenger RNA (mRNA) into polypeptide chains. They are composed of ribosomal RNA (rRNA) and proteins and can be found freely in the cytoplasm or attached to the endoplasmic reticulum, forming rough ER. Ribosomes play a vital role in cellular function, as proteins are essential for various biochemical processes, including enzymatic activity, structural support, and signaling.