It's one of those things where you can take a simple tool and probably make something hideously complicated with it if you go too far, but in simple cases it's useful all over the place.

For example, I very often write functions that take an initial parameter representing some sort of customisable context and then further parameters that are the right types to use with some standard higher order function like a map, filter or fold. Partial application then supplies the context and gives back something ready to pass into that HOF.