Quick units have 1 extra movement point, but 5% less HP than usual. Quick is the most noticeable trait, particularly in slower moving units such as trolls or heavy infantry. Units with the Quick trait often have greatly increased mobility in rough terrain, which can be important to consider when deploying your forces. Also, Quick units aren't quite as tough as units without this trait and are subsequently less good at holding contested positions.
Units with the Quick trait get an extra movement point per turn. This can be very important when moving through difficult terrain such as water or caves. It can make the difference between being able to move one hex or two. ~Kalenz~