Why are peroxides explosive?
I don't like to speak in generalities if I can help it.

But we can talk, for instance, about hydrogen peroxide. One of the most familiar schemes is a disproportionation where,
$$2 \ce{H2O2} \rightarrow 2\ce{H2O} + \ce{O2}$$ 
and as you study this particular species, you will see this reaction more and more often. Actually in solutions of hydrogen peroxide you can take a 30% concentrated solution and add some Mn and subsequently measure a significant increase in oxygen concentration over time. Although you should know the solution itself decomposes slowly in practice when exposed to light or due to trace impurities, but this pales in comparison to the case involving a catalyst. This reaction is, in part, why researchers believe a peroxide-type species is important for the Oxygen Evolving Center of Photosystem II. Another fun demonstration of this process is often where foam is generated from a large graduation cylinder, see here, upon addition of KI.

Now 30% is weak, if instead you look at 80% solutions you will notice that the decomposition will evolve steam because it is so exothermic. In fact, the first liquid-fueled rocket in 1939 used an 80% concentrated solution and decomposed it with calcium permanganate. Later engines utilized another important property of hydrogen peroxide for its decomposition until around 1980: the fact that it is a stronger oxidizer than chlorine/chloride.

Thermodynamically we say the disproportionation is favorable since it has a fairly negative (~ -100 kJ/mol) enthalpy change and a considerable change in entropy ( ~ + 70 J/(mol K)). The basis of this is that it is highly favorable to form dioxygen and this is a large driving force of this reaction in terms of enthalpy and entropy. You'll also see this danger in species that are really close to forming dinitrogen too, see here and here. It only takes a catalyst for this down-hill process to take off. Which could be quite deadly if unintentionally concentrated and then introduced to a catalyst in a closed system. Perhaps the story is similar for other peroxides.