What you Need
What to do
Obviously be careful with the candle, and as the balloon may burst, do the experiment away from anything electrical, or which may be damaged by getting slightly wet. Don't leave the balloon over the candle for more than a few tens of seconds or the water could get very hot.
What may happen
You should find that the empty balloon pops immediately, but the balloon with the water is stable for ages over the flame.
Why does it happen?
The candle is a source of heat and will add heat energy to any object it touches. If this is well thermally insulated like the rubber in the balloon, the object will heat up to many hundreds of degrees Celsius. Rubber can't cope with these temperatures and it fails, causing the balloon to pop.
If there is water in the balloon the heat can be very efficiently transferred to the water. Water takes a huge amount of energy to heat up, so it stays relatively cool for a long time, cooling the balloon and stopping it heating up.
In fact if there is any liquid water at all, it must be at below 100°C as otherwise the water would boil absorbing even more heat.