BF3 (Battlefield 3) is a first-person shooter game made by DICE company. It means that those drivers are specially optimised to run this game.
Verde are drivers that are designed for notebooks only (so NVIDIA M-series).
Modded drivers are, well modified drivers... Some graphics cards are not supported by NVIDIA drivers, allthough they are just regular NVIDIA cards - the driver just won't install. The modded drivers should install properly on any NVIDIA card. So if official WHQL drivers give you "card not supported" error - go for the modded ones. Else just download and install the official ones.