Vinyl polymers are made up of multiple (hundreds, thousands, even MILLIONS) of alkene subunits concatenated together into long chains. They have a wide range of uses from packaging (polystyrene a.k.a. styrofoam) to fibre (PVC) to nonstick surfaces (teflon).
Alkenes can be added together into long chains because of their carbon double bond, denoted “C=C.” This bond is rich in electrons, which means it can join readily to an electrophilic (“electron loving”) reagent.
Radicals are just such electrophiles. Whereas most valence electrons exist in pairs, radicals have solitary valence electrons. But electrons were never born to be lonely, and will do everything in their power to find a partner! Since the C=C bond has plenty of electrons, it will happily donate one of them to an approaching radical, thus forming a single covalent bond.
In doing so, the double bond opens like a drawbridge. However, while one Carbon is now bonded happily to the (former) radical, the other Carbon has been left in the lurch with only 3 covalent bonds - since it had nothing to which it could donate its electron, the electron simply returned to it. So now that Carbon has only 3 bonds, which simply won’t do. However, it also has a very special asset: the lone electron. The Carbon itself has become a radical, ready to attach to another electron-rich C=C bond! It finds just such a bond in another alkene subunit, which it bonds with to form ANOTHER radical. This whole process is known as “propagation.”
This chain reaction continues on and on and on until 2 radicals bond to each other. Since no further radicals are produced, this process is known as “termination.”