To summarise it quickly, Chomsky's contention was that all the world's languages can be described by shockingly few degrees of freedom on the same universal grammar, and that we learn language surprisingly fast relative to training data because all we are really picking up are those parameters and the rest is hard wired from birth the same way horses come out the womb already hard wired to gallop.
Decades later, very few things have truely stood the test of being universal among languages, but it was still a valuable contribution because he poked a serious hole in the pure Hebbian reinforcement theories which were in vogue back then.