Even without any dialogue, it takes less than one minute for the Koldunov Brothers to illustrate how the balloon trick works in the above video. While it may not be the most efficient or elegant solution out there, we cannot argue with its effectiveness: portraits shot using the balloon to diffuse the light look dramatically different than with the bare flash.
The main reason why on-camera flash typically looks so bad is that the size of the light source is very small. This creates harsh shadows that fall directly behind your subject and leads to the “deer in the headlights” look. (This is true even with expensive external flashes, not just the built-in pop-up flash.) To improve the quality of light, it needs to be diffused over a larger surface. While many purpose-built accessories exist for doing this, none are as inexpensive as a latex balloon — and few provide the same level of diffusion.
Generally speaking, softer (or more diffuse) light looks better and the larger the diffusion surface, the softer the light. But on-camera flash diffusers have limits on how big they can be, as they also need to be portable. That’s the brilliance of the balloon. It fits in a pocket, yet expands to be as large as you need it.
The downside of this trick, beyond making yourself look a little ridiculous, is that the balloon could introduce a color cast to your flash if it’s not pure white. Then again, while we’re on the subject, experimenting with different colored balloons might yield some pleasant surprises.