Carbon-carbon p-bonds are prone to electrophilic attack - in a process which breaks the p-bond and simultaneously forms a new s-bond between the electrophile (electron deficient reagent) and a carbon atom of the original p-bond. The other carbon of the p-bond becomes a cation - and is activated which further reacts with another alkene monomer. The polymer continues to add monomer very rapidly until all of the alkene is consumed. Both cations and radicals are electron deficient and can both initiate addition polymerisation.
There are several major types of thermoplastic polymers - high and low density polyethylene, polypropylene, polystyrene, polyvinyl chloride, and many more - all of which are addition polymers: