So we gots ethylene, #H_2C=CH_2#, an unsaturated organic molecule. Under given conditions, and typically this is catalyzed by a transition metal complex, these so-called ethylene #"monomers"#, are clipped together to give a long chain polymer....
#nH_2C=CH_2 stackrel("catalyst")rarr{CH_2-CH_2-CH_2-CH_2}_(n/2)#
...i.e. #"polyethylene..."#
Other olefin monomers can also be utilized; for instance, propylene, #H_3C-CH=CH_2#, or styrene, #C_6H_5CH=CH_2#...and the polymerization of these materials can lead (in the best circumstances) stereoregular polymers in which the individual monomers are clipped together in a precise geometric relationship.
Alkynes can also undergo polymerization, but in general this is easier to do....but it is hard to find an application for these poly-olefins....