One of the mathematical fields string theory is said to have had a large bearing on is enumerative geometry which, roughly, deals with counting rational curves on hypersurfaces and its generalisations. From what I could surmise, its main relevance in string theory is in enumerating the rational curves on the quintic three-fold, a particular type of Calabi-Yau manifold, but I have no idea what this entails (though an educated guess would be to obtain desirable properties during compactification).

Could someone illustrate (even a high-level overview) why this is useful, preferably in a manner to someone (like me) who is not well-versed in string phenomenology or Gromov-Witten theory?

One of the mathematical fields that string theory is said to have had a large bearing on is enumerative geometry which, roughly, deals with counting rational curves on hypersurfaces and its generalisations. From what I could surmise, its main relevance in string theory is in enumerating the rational curves on the quintic three-fold, a particular type of Calabi-Yau manifold, but I have no idea what this entails (though an educated guess would be to obtain desirable properties after compactification).

Could someone illustrate (even a high-level overview) why this is useful, preferably in a manner to someone (like me) who is not so well-versed in string phenomenology or Gromov-Witten theory?