Things float because they're less dense than what's around them.
When the car's stopped, or moving at a constant rate, the balloon floats straight up.
If the car accelerates forwards, everything attached to it goes too, but the air isn't nailed to the car, so it sits where it was. However, it can't completely squash itself onto the back window - one of the properties of gases is that they tend to spread themselves out evenly if left on their own.
So what happens is, the air gets slightly denser towards the back of the car while the 'push' of acceleration is on (really, the car's just racing off and the air's not coming along at the same rate just yet).
This makes the balloon 'float' towards the front of the car. If it was heavier than air, it would go backwards, but in this case, it's lighter, so acts as an accelerometer (points in the direction of acceleration).
You can make an accelerometer by putting a bit of styrofoam in a jar of water held on its side. Whichever way you accelerate the bottle, the styrofoam will go that way too, because the more dense stuff lags behind and therefore pushes the less dense stuff out of the way.