Based on the claims in the media, it sounds like the idea was to mix H2O2 (hydrogen peroxide, but not the low test kind you get at the pharmacy), H2SO4 (sulfuric acid, of necessity very concentrated for it to work at all), and acetone (known to people worldwide as nail polish remover), to make acetone peroxides. You first have to mix the H2O2 and H2SO4 to get a powerful oxidizer, and then you use it on acetone to get the peroxides, which are indeed explosive.
A mix of H2O2 and H2SO4, commonly called "piranha bath", is used in orgo labs around the world for cleaning the last traces out of organic material out of glassware when you need it *really* clean -- thus, many people who work around organic labs are familiar with it. When you mix it, it heats like mad, which is a common thing when you mix concentrated sulfuric acid with anything. It is very easy to end up with a spattering mess. You don't want to be around the stuff in general. Here, have a look at a typical warning list from a lab about the stuff:
clipped from: www.pridestomb.com