OH! I think I get it! I just read the link by jusdooit - it's very helpful and simple for a noob like me.
Let's see if I have this right - I could just leave the cogs in the middle range and shift between the rings all I wanted. That would make big changes and be kind of like it is now when I switch between the 3 gears I have on my 3-speed beach cruiser. If I was down in the lowest ring and it was still too hard to pedal up a hill, then I could start going down on my cogs. Or, if I was up in the highest ring and still spinning out going downhill, I could go head and start moving up on my cogs. What I don't want to do is get all the way down to the lowest cog before I switch down to a lower ring, or up all the way to the highest cog before I switch to a higher ring because then that would make the chain crooked and the bike wouldn't ride smoothly.
The cogs are for subtle changes and the rings are for big changes.
Right?