A gear ratio is basically "input : output". Meaning if you had a 2:1 gear ratio, it would take two revolutions of the input gear to make one revolution of the output gear. Imagine a bike with multiple gears. The least strain on who's pedaling comes when they have the smallest gear on the pedals, and the largest on the rear wheel. This is because it take many turns to move the rear wheel a certain distance, but you can't go quickly. And the opposite when you have a large pedal gear and a small wheel gear, one rotation of the pedals will make the rear wheel spin more revolutions in the same time, giving you more speed but also more strain on who's pedaling.
The notion of needing to "change your ratios" because of larger tires just implies that because your engine (the bike pedaler) is having to work harder to turn larger tires, it would help to have gears with lower ratios ( lower would be 5:1 as opposed to 2:1 ) to lessen the strain on your engine and improve acceleration. And due to the fact that its harder to stop larger tires, it would also help to have larger breaks. Both breaks and different gearing, are not necessities, but they would help. Nope that clears up some stuff about ratios.