What are 13 oz copper PCBs used for?
The super thick copper on PCBs is to handle large currents.
At high currents it is important to pay attention to voltage drop and temperature rise in your traces.  The thicker the copper, the better, because more cross-sectional area means less resistance.  Less resistance means less voltage drop and less heat (therefore less power loss as well).
According to Epec (a PCB manufacturer) they use a combination of etching and plating to achieve extreme thicknesses with accuracy (allowing tighter tolerances).
Here are some example pictures of extreme copper on PCBs:

source: epectec.com

source: hackaday.com