What really helps to understand the gears: turn your bike upside down (or better, put it in a stand if you have one). Watch what happens to each cog and the wheel as you turn the pedal. Get someone to help you shift it into another gear (you don't need help if you have it in a stand--your toddler can help turn the pedals while you do the shifting if you have it upside down), and see what happens. Turn the pedals yourself in each gear, you'll see how it's hard to turn the pedals when it's a high gear ratio and easier when it is a low gear ratio.
2009 Trek 7.2FX WSD, brooks Champion Flyer S, commuter bike