To polymerise something is to link together a lot of similar small molecules into a long chain.
The similar, small molecules are called monomers. These are the single chemical units that are linked together - mono means one.
When they form a sufficient, repeating chain, they become known as a polymer, through the process of polymerisation - the joining together of monomers.
Examples of polymerisation are when ethene bonds with other ethene molecules to make polyethene, a common plastic. Amino acids also polymerise and make a long chain known as a polypeptide or protein.