We can add specific molecules to our reaction if we want to prevent or slow down polymerization. For example, when you purchase a commercially available monomer from a supplier, you may read on the bottle that the monomer is stabilized, perhaps by a molecule such as MEHQ (monomethyl ether hydroquinone). Such inhibitors are added to extend the shelf life of the monomer by preventing unwanted, premature polymerization. Inhibitors work by "trapping" any radicals that are generated in a very stable molecule that does not further react. If a "normal" polymerization follows a trajectory such as in Figure 5.6 (Figure 4.7 in the textbook), then that same polymerization with an inhibitor present would follow a trajectory like Figure 5.6 (c); the inhibitor prevents polymerization for a certain amount of time (the induction time), which depends on how much inhibitor is present. As soon as all the inhibitor is used up, then the reaction proceeds as normal.
A retarder works slightly differently than an inhibitor, and serves to slow down a polymerization rather than prevent it, as shown in Figure 5.6 (b). Retarders act in a similar way as inhibitors in that they stabilize radicals, but are not quite as good as preventing further reactions of the radicals as inhibitors. Hence, polymerization can still proceed in the presence of active retarder.
Introduction to Polymers, Third Edition, CRC Press, 2011.