Any good telescope can change it's magnification by simply changing the eyepiece. The easiest way to understand light gathering is to think about the pupil in your eye. On a sunny day it gets small. In the dark it gets big, that lets more light into your eye so that you can see better in faint light, but your eyes can only get so big. This will allow you to see very faint objects.
Resolution is perhaps the most difficult to understand.
At first it may seem to be the same as magnification, but it's not. Resolution is the ability to see fine detail. A telescope's resolution is determined by its aperture, not its magnifying power. For example when you view a double or binary star with an 8 inch telescope you can clearly see it is two stars at say 50 X, but if you look at the same star system with a 4 inch telescope at 50 X again, you may not be able to split the pair of stars, even though it's the same magnification. It requires more light to be able to split those close binary star systems.