We will start with differential gears.

When people talk about the gear ratio of a differential they are talking about the relationship of two gears inside. The ring and pinion (R&P). The ring gear attaches to the carrier and is the larger gear in the diff. The pinion is what sticks out the front of the diff and the driveshaft yoke attaches to.

Here is a picture of a R&P.

So now you know what gear is what and what they look like, we can talk about the ratio. This is simply a correlation between the number of times the driveshaft turns (pinion) to the number of times the wheels turn (ring). A ratio is written as 3:1. The 3 is the number of times the pinion gear turns for every 1 time the ring gear turns. So a 4.10:1 gear ratios means the driveshaft will turn 4.10 times for every one time the wheels turn.

Now, the ratio is calculated by dividing the number of teeth on the ring gear, by the number of teeth on the pinion. This means that as the gear ratio gets lower (numerically higher number), the weaker the gear set becomes (more specifically the pinion). For instance, the ring gear of a 4.10 gears will be smaller and the pinion will be larger than the same gears in a 4.88 gear set.

Now, why regear.

There are a few reasons to regear your differentials. Since tire size will change your final ratio. This is why tire size effects your final ratio and why you will notice a loss in "power" when you move up to larger tires. If you have 30" tires and you travel at 65MPH at 2000RPM's, when you increase your tires size (say to 33"), it will take more engine RPM's to make the tires travel at the same speed. You can change your differential gears to make up for this loss. Same goes for off-road, you can use lower ratio gears to lower your final ratio and allow you to crawl through the woods.

So, for highway cursing use, you want a higher gear ratio so the engine has to work less to maintain a higher rate of speed (this is the purpose of the overdrive in the transmission).

For off-roading, you want a lower gear ratio so that even at high engine RPM's, the wheels will turn slow allowing you to crawl over rocks (this is the purpose of the low range in your transfer case or lower gears in your transmission).

Hope this makes some sense for the folks that previously didn't understand gears and gear ratios. If anyone sees any mistakes, please let me know. If anyone needs any clarification on something, let me know.