An army heals one unit at a time. If it's in a barracks each unit heals during one turn of inactivity. If there's no barracks it heals one hit point at a time for each turn of inactivity, so a redlined army can take 10 turns to heal instead of two or three turns for individual units.
I believe armies are powerful in Conquests, as they get an extra movement point and extra strength points. I never thought of them as particularly effective in vanilla or PtW, for the healing reason above, and because they constrain your fast units to all attack the same target, which may not be what's best.
Their two advantages over separate units are that all units stay alive until the whole army is killed, and the AI looks at the best unit's hit points in deciding whether to attack a stack. If the best unit is an army with 12 hit points the AI will almost never land attack, whereas 4 hit points for each unit makes a softer target. So an army provides excellent cover for a pillaging force, or to defend an attacking force. The AI *will* bombard an army, though, and if it can knock it down to low hit points it will then attemopt to kill it.