Why is it important to describe the resonance structures in molecules such as ozone, O_3, and the organic molecule benzene, C_6H_6?

Ozone is a bent molecule. That's the experimental fact. A Lewis structure of $O = \stackrel{+}{O} - {O}^{-}$ in which there are 3 regions of electron-density around the central atom explains this geometry. It also explains the trigonal planar geometry of $C {O}_{3}^{2 -}$. The benzene molecule, ${C}_{6} {H}_{6}$, crops up persistently in organic chemistry. It is reactive under certain circusmtances, but not as reactive and not reactive in the same way as an olefin or an alkyne.
Our ideas of resonance can help rationalize the observed reactivity. The idea of $6$ $\pi$ electrons delocalized around a 6-membered ring can be extended to inorganic chemistry. Borazine, ${B}_{3} {N}_{3} {H}_{3}$, a benzene analogue, is isostructural and isoelectronic with benzene, and has similar aromatic chemistry.