Polymerization and the break down of a polymer are two opposite reactions. what role does a water molecule play in both of them?

A polymer is a large molecule made up of smaller molecules called monomers. The process of monomers joining each other to create a polymer is called polymerization. Water plays a role in condensation polymerization. In this reaction a hydrogen from one monomer will connect with the hydroxyl functional group of another monomer. The two join and water is formed. the water breaks off, leaving the remaining functional groups of the  monomers able to be joined together.
Hydrolysis is the opposite reaction where water is added to the polymer. The hydrogen (H) and hydroxide (-OH) react with the functional groups that formed the bond and as a result break apart the polymer.

As what he you go get the hot dog ; )