It's a pretty simple reaction, the decomposition of hydrogen peroxide solution into water and oxygen gas.
H2O2 (aq) --> H2O (l) + O2 (g)
This reaction happens all the time, most commonly in your home in that brown bottle of 3% hydrogen peroxide solution that somebody bought years ago and that goes 'pfsssst' whenever you open the cap.
The 'pfsssst' is the built-up oxygen gas.
In the demonstrations below (and after the jump with much bigger volumes), that reaction is catalyzed (sped up) by the addition of various things - typically sodium or potassium iodide but also yeast. And the oxygen gas is contained within soap bubbles.
Add that all together - maybe add in some food coloring - and you get a foamy mess.
...on Jimmy Kimmle's show...
...on The Big Bang Theory...
...a supposed world record volume...
...another supposed world record volume...
...another supposed world record volume...