Aspect ratios are the size of the horizontal dimension of the screen relative to the vertical. Reading that sentence again, the explanation seems more difficult than the thing it's trying to explain. In simple terms, divide the larger number listed (x, or the horizontal resolution) as the resolution by the smaller (y, or the vertical resolution), and you'll have a value that will give you the aspect ratio.
For example:
A 1024x768 monitor: 1024/768 = 1.33333, so you have a 4:3 ratio screen.
A 1280x1024 monitor: 1280/1024 = 1.2, so you have a 5:4 ratio screen.