A polymerisation reaction is a reaction between monomers to form polymers, such as ethene --> polyethene (@Vegemite, ethylene is another name for ethene).
i.e. H2C=CH2 + H2C=CH2 + H2C=CH2 + H2C=CH2 --> -CH2-CH2-CH2-CH2-
This reaction is addition polymerisation as the monomers are "adding" together by the splitting of double bonds.
There is also condensation polymerisation, such as the condensation reactions between monomers such as amino acids to force a polymers such as proteins. Proteins are held together by peptide (amide) bonds (represented by -CONH-)
H2N-CZ-COOH + H2N-CZ-COOH + H2N-CZ-COOH + H2N-CZ-COOH --> H2N-CZ-CONH-CZ-CONH-CZ-CONH-CZ-COOH + 3 H2O (each condensation reaction produces a water molecule)
Z represents a variable side chain, H2N = amino group, COOH = carboxyl group.