A polymer is a substance made of very long molecules. Each long molecule is built from a small unit that repeats over and over again, joined together by covalent bonds.
The small molecules that join together to make a polymer are called monomers. Many hundreds or thousands of monomer molecules link up to form one polymer chain, so a polymer has a very high relative molecular mass compared with its monomer.
The chains in a sample do not all have the same length. For this reason we talk about the average relative molecular mass of a polymer. A polymer is therefore a substance of high average relative molecular mass, made up of small repeating units.
Poly(ethene) is an example. Its monomer is ethene, and the ethene units repeat along the chain.