In my novel(Villainess and Grimoire), I use it for a few different things, some self-explanatory others like increment of magic damage, understanding of the world like some people mentioned, but also of skills, for non-human races, I also use it(especially) for beasts with low int to not being able to talk, whereas those with high int can talk without issues.
Int also goes towards the perception of the world such as mana, how it influences, how it can be controlled, and of course, the skills that require that energy, whereas wisdom, is mana max capacity plus the wisdom to not do things stupidly.
In what comes to mana, higher int would also condition the number of magic spells/skills one could use at the same time, as well as how much mana one would be able to control in one go.
I hope that helped a little~!