Why is nylon durable and how does it have such exceptional strength?
Polyamides (such as Nylon) are molecules containing a large number of amide functions: 



In those functions, the $\ce{C=O}$ bond is polarized (due to the difference in electronegativity between C and O) : $\ce{^{\delta+}C=O^\delta-}$.
The N-H bond is polarized, too: $\ce{^{\delta-}N-H^\delta+}$.
This leads to H-bonds between the chains: 



While H-bonds are weak interactions, their high number (as there are a lot of amides in polyamide chains) leads to strongly bonded chains, which results in increased strength and durability.