Inflate and tie off a balloon. CAREFULLY hold it over a candle flame, and... POP! Now fill a new balloon with water, and tie it off. Hold it the same height above the candle flame... it doesn't pop!
The balloon pops if the wall of the balloon gets hot enough to melt. In the case of the air-filled balloon, the balloon wall definitely heats up enough to melt. Even though the outside of the water balloon is near the hot candle flame, the inside of the balloon wall is touching cool water. The water keeps the balloon wall from getting hot enough to melt, so it doesn't pop.