Aerodynamic Downforce is a dynamic load pushing down on the car as speed increases, the higher the number, the more grip.
Downforce: (Does affect PP)
If you are not restricted to a PP limit, higher downforce settings often produce the fastest lap times, especially on a track with a lot of corners.
At higher speeds higher downforce settings reduce top speeds so at some tracks with long straights like LeMans (no Chicane), Tokyo Expressway and Special Stage Route X may benefit from reducing downforce and therefore drag.
Road cars benefit greatly from adding downforce, especially rear downforce to stabilise the car at higher speeds. You can buy Aero parts from GT Auto which allow downforce to be tuned on road cars.
If you are PP restricted tuning to 600pp, 700pp or 800pp then the trick is to have Maximum Rear Downforce and almost Minimum Front Downforce (tune to the PP number) because having the car suffer mild understeer at high speed allows a lower PP which you can use to add more power back into the car. This results in much faster lap times and race times at Sardegna WTC800 and Tokyo Expressway WTC600 for example.