What purpose do chain reactions serve?
[...] it would be great if you could support your answer with a real world example or application.


Free radical polymerizations of monomers with $\ce{C=C}$ double bonds are not completely useless ;) 

Let me give some examples:


Polymethyl methacrylate (PMMA) is obtained by polymerization of methyl methacrylate (MMA). Think acrylic glass.
Styrene can be polymerized to polystyrene (PS). Think Styrodur and food containers.
Vinyl chloride is polymerized to polyvinyl chloride (PVC). Think pipes, insulation for electric cables, flooring.