Tell us about yourself!
Hydrogen Peroxide is H202 (two hydrogen atoms, 2 oxygen atoms). The yeast acts as a catalyst, separating the H202 into H2O + O (it splits into water and oxygen). This reaction also releases heat.All this heat, water, and oxygen creates steam. Because you added dish soap, the rising steam makes bubbles (foam).
In another article about this, meant for science classes, they suggested an experiment to demonstrate your point. Light a match and then blow it out. Right away (before the match can cool), hold the match just above the foam - the influx of oxygen should reignite the match if there's any ember left in it. I imagine this works better if you hold it above the tube the foam is flowing out of.