I have played quite a few games where my opponent did not expand at all. I crushed him easily. When you expand you can double your resource collection rate and therefore double your army. I expand to at least 2 or 3 expansions in any of my games. Some of my opponents who did not expand where making units very slowly and only a few production building. I was able to create a large sized army in a matter of 2 minutes. That might be because I was zerg, but also because I had much more resources.
How to know when to expand: Always expand when you think you have the upper hand. For example, if you just harassed someone and killed half their workers, that is a perfect time to expand because they have to get their economy back in shape. When you have a clash with their army, and yours comes out on top, they will be too busy making units, so thats another good time to expand.
Ask me any other questions, I cant seem to think of anything at the moment.