"Questing" the stats means doing quests in which the rewards are experience for that skill.
The reasoning behind is that those quests are usually needed for low combat level pures or are prerequisites for better quests. For example, getting to experiments requires preist in peril and one other one... can't really remember atm.
It's useful for zerkers to quest their defence, dragon pures to quest their attack (dscim) and all pures to quest their prayer.
EDIT - if that's not clear... the quests give levels in which you don't want after you already get the level you need. Prayer needs to stay low, so imagine getting prayer at 52 (pure maxed) and then realizing you need to complete a quest for DT that raises it to 60.