Spider gears are an integral part of you differential. They are part of the gear set that allows your rear wheels to turn at different speeds, which is necessary for many instances. When your vehicle goes into a turn, the out wheel turns at a faster rate than the inner wheel; this is accomplished through a series of gears including spider gears.
Spider gears offer you the ability to turn your vehicle without feeling the rear end bump as you go around a turn. If it weren't for spider gears and side gears within the differential, both rear wheels would turn at the same speed. If you're only going straight, this is not a bad thing, but the moment you go into a turn, the outside wheel will try to speed up. If spider gears and side gears where not in place, that outer wheel would not be able to turn faster than the inner wheel and would actually drag as you went through the turn, producing a bumping, lurching motion.
Spider gears are provided in the differential from the manufacturer and are one of the many shapes that gears can come in. Unlike spur gears, spider gears meet the shaft or other gear at a right angle, allowing them to be seated on shafts that do not touch and allowing the differential to be smaller and yet provide the necessary performance for most applications. Aftermarket, or performance differentials, have differently sized spider gears as well as differential housing to provide better traction for harder usage.
Spider gears are employed in limited slip differentials as well as standard differentials. Within a limited slip differential, spider gears work in conjunction with clutch packs to reduce the speed of a wheel that is spinning much faster than the other. The purpose of the clutch packs is an attempt to keep both rear wheels at relatively the same speed. Their efforts aren't noticeable when you're simply taking a curve, but if one wheel where to be placed on ice or in slick mud, the opposite wheel would be able to grip the road.
A standard differential allows all the torque to go to the wheel with the least amount of resistance; while this isn't a bad thing for street driving, if you intend to take your vehicle off road, or consistently drive in areas where little traction and slick spots are common, a limited slip differential, or fully locking differential is a better choice. The spider gears within these differentials are much larger and made much thicker than they are within standard differentials. With a standard differential, the wheel that has the least amount of traction will get the largest amount of spin, leaving your vehicle sitting still. A limited slip differential is designed to stop that, allowing much more torque to go to the wheel with traction.
Spider gears are one of the modern innovations that allow limited slip differentials to operate. Interestingly, they also play a vital role in locking differentials and standard differentials, as well.