People change gear ratios in differentials to accomplish different things.  Driving larger tires, faster quarter mile times and let's not forget, "better gas mileage".  But what exactly changes in your differential to make that happen?  

The Ring & Pinion:  Changing the number of teeth on the ring & pinion gears will give you different ratios.  Both gears on the left are for a Chrysler 8.25" axle.  The gear on the left is a 4.56 and the gear on the right is a 2.71.  The 4.56 gear set has a thicker ring gear and smaller pinion tooth count to archive this ratio.  The 2.71 has a substantially thinner ring gear and larger pinion.  It is important to note that both of theses gears use the same "Carrier" to achieve this wide ratio change.  

Carriers:  Sometimes manufactures use different carriers to accommodate larger or smaller pinion gears.  (Called a "Case Break")  The "mounting deck" that the ring gear rides on can move toward the center of the differential for a small pinion, like the 4.56 or shift outward in the direction of the wheels for a larger pinion, like the 2.71.  Sometimes this can cause additional cost to a gear change.  But usually this gives you an opportunity to add a limited slip or locker while you change gears.