Side gears sit inside the differential carrier. They mesh with the smaller spider gears. As the car turns, the spider gears spin on their shaft. This lets the side gears rotate at different speeds. This prevents the tires from scrubbing when you turn corners.
Worn splines on side gears will cause power loss to that axle. The axle shaft will slip inside the gear. You will hear grinding noises when trying to accelerate from a stop.