"Her" is not just a possessive pronoun, it also functions as the object form of "she." Just as you would say, "Give her a cup of coffee," you would say about a car or wineglass, "Fill her up." Now, these are things, not women, so it would be more logical to say "fill it up." However, since many men refer to their car, boat, plane, etc., as a female entity, the phrase "fill her up" became standard when asking for fuel, and it has carried over to other things (e.g., wineglasses).

Talking about filling a glass, I'd rather use "it" as possessive pronoun, not "her". Unless you are talking about filling up a gas tank.