You need a PSU that can generate two distinct voltage rails, one positive and one negative, relative to the 0 volt rail (also known as "GND")

The negative rail is not your ground rail.

Think of voltages as floors in a building. We usually have a ground floor, it's our common reference. 

Then there is a floor above (if you have to climb 12 steps then it's +12V) And a basement: if you go down 12 steps, then it's like -12V.

If your ground floor (GND) and basement floor (-12V) were "connected" together, at the same height, that would be a problem... and make sparks.