A buff is just an effect that improves your stats. For example the warrior skill Ironblood is a buff that raises (buffs) your armor by 50 points for 12 seconds.
A root is an effect that holds the affected target in place. The archer root skills do this, and the mage freeze skills essentially root as well. Stun differs in that the target is not just immobile but completely incapacitated, unable to move or act.