Being new to GIS and Open layers I spent a long time trying to make sense of what resolution is. Finally, I think I have a fair idea of what resolution means in open layers world.

Resolution is nothing but a way of saying how much your map units vary as you move on the computer screen.

Say, you want to represent a map bounded by ( -180,-90,180,90) in a window of dimension 256×256. Now, how do you calculate the resolution?
Since the map extends from -180 to +180, you have to fit a total of 360 degrees in a screen of size 256. That is, your resolution is 360/256=1.40625.