Those are descriptions of screen resolutions, or how much you can see on the screen at the same time. The higher the resolution, the more you can see at once and also the smaller text appears.
The best resolution depends on your screen size, what you do with your computer, and your vision. Smaller resolutions are better for gaming, watching standard DVDs, and for folks who are farsighted or have vision problems. Larger resolutions are better for multitasking, watching content in high definition, and working with pictures, drafting, or other large-format images.
The other difference between the resolutions you mentioned is that one is "standard" 4:3 ratio, and the other is widescreen. Widescreen resolutions are becoming increasingly more popular since it's easier to negotiate extra screen space to the side of an application than to negotiate extra screen space on the top or bottom of an application. This means more "room" on the sides is more conducive to getting more done at once than more "room" on the top and bottom.