The control arms locate the axle. If you didn't have them the axle would fall out of the car. That's pretty simple.
The job of the lower control arms is to push the car by transmitting force from the tires to the frame. However, this leaves the axle free to move side-to-side under cornering loads and also to twist up or down along the axle centerline under torque. The upper control arms are designed to serve both functions.
The problem is that the geometry offered by the stockers is severly compromised. Under light duty, they are acceptable- but when pushed they don't perform well at all. Since the geometry inherently wants to bind up, the only way to prevent binding is the use of squishy rubber bushings. Squishy suspension components and high limits of adhesion are not allowed to occupy the same space at the same time. Its like the Pauli Exclusion Principle. Aftermarket pieces are usually stronger/stiffer and with harder bushings.
There are reams of write-ups about suspension work. I suggest you do some searching here, or on How Stuff Works, or at Maximum Motorsports, or at Corner Carvers, etc. to give you some basic working knowledge. Get detailed later.