This is very simple, if you just look at the Wikipedia page for polymer you will find the answer.
Polymers are just very long molecules, made up of repeating smaller molecules conected end-to-end. We call the smaller molecules 'monomers'.
Amino acids are a type of monomer. When joined up, they form polypeptides. These polypeptides, when made to curl in the right way, form proteins, which do perform lots of functions in the body e.g making muscles, making cells, making enzymes..