What exactly is the purpose of using a clay bar on the exterior?

It take the little bumps out of the paint... if in fact you have them

3M makes a kit. The label says:
"Safely removes overspray and paint contaminants
Use with water-based lubricants
Effective on paint, glass and chrome"
A spray bottle of lubricant came with the bar in a kit.
I had a bodyshop repair collision damage to my car but they got overspray on the rear wing. I used the kit to clean it myself rather than go through the hassle of taking my car back and waiting... you know what I mean...