Let's say your tires are supposed to be filled to 35 psi. If they are filled correctly, six square inches of your tire are touching the road, just the way your tires were designed. But let some air out, and now the pressure is only 30 psi. Since your tire is like a balloon, the more air you have on the inside, the rounder and more firm your tire becomes. If you had six square inches touching the road at 35 psi, the flatter 30 psi tire will have eight square inches touching at once, making it harder for your engine to get things rolling from a dead stop. Here's another way to think of it. Say your dog is going to the vet, and she's not so interested in moving toward the car, so you pull. You start out pulling her with all four of her feet on the ground. We'll call this four square inches touching. But then she plops her rear end on the ground. You're now pulling 12 square inches, and boy is she harder to drag toward the car.
Unfortunately you can't dangle a piece of salami in front of your car to make it go, so you're left using the engine, which uses more gas the harder it pulls. Filling your tires to the correct pressure will make it easier on the engine, and that means you'll be using less gas. It can make a difference of a three or four miles per gallon. That's at least 36 more miles to the average tank of gas. At one tank of gas per week, you could be adding 1,872 free miles in a year! That's savings, and that's Automotive Empowerment for no money at all.