The white fluffy clouds are fog, of course, but for barb spawning purposes, the greyed out areas are also fogged (since you don't have real-time sight on those tiles). Best sentry to suppress barb camp spawns is a scout with scouting I promotion (even better with scouting II or III).
EDIT: And, for what it's worth, barbs are more troublesome at Prince and lower levels since the AI is so sluggish to expand (and therefore slow to fill up barb space) and the human player can't possibly deploy enough units in foggy areas to suppress barb spawns.