understanding resolution and aspect ratios

[Andy in NY]

Let me preface by saying that i just spent all damn day reading the "black bars" thread, and this certainly isn't what i'm asking about.

But recently I bought an apple tv and am transfering all my dvds onto it. Im using handbrake to encode them. I notice that there are 2 things when it comes to the picture... aspect ratio and then theres another number... usually 8** x 5** or 1028 x 720 (those are just random numbers, not specifics). what do those numbers mean? I suspect something to do with resolution, but i'm not sure. if they are having to do with resolution, can i change them to "upconvert" the picture quality? i notice a difference between viewing them from an upconverting dvd player and watching them on the apple tv.