I did a little research on ammonium tri-iodide, and explosives in general. Basically, the force of a conventional explosive is based on the number of nitro groups a given molecule has. TNT, for example, has 3; Octanitrocubane has a whopping 8. Ammonium tri-iodide is NH4I3, so it only has one nitro group. Per mole, it therefore has much less explosive force than others-- in fact, it'll be one of the weaker ones, since you can't get any less.

However, stability is based on molecular structure. Octanitrocubane, for those who know basic chemistry, consists of 8 carbon atoms in a cube structure. Since carbon likes to have 4 bonds, that leaves one bond each free to attach a nitro group. It helps if you can draw the Lewis dot diagrams. As a result, it's highly stable-- despite the fact it has over twice the explosive force of TNT, it's so steady you could hit it repeatedly with a hammer, and never set it off.

Now, nitrogen likes to have 3 bonds-- thus ammonia is NH3. However, our formula calls for NH4-- ammonium. Now, ammonium isn't exactly stable to begin with-- it tends to only exist linked up with other molecules, making it a stable-ish ion. (It tends to get rid of that extra Hydrogen in a real hurry, although it doesn't exactly break free either.)

So, we now attach 3 iodine atoms to an already unstable ion. Using basic valence chemistry, we see that Ammonium has a charge of -1, while Iodine tends towards a +1 charge. So, NH4I would be nice and stable-- but we're attaching 3 Iodines. As a result, the whole thing is more than a little unhappy at the world, and will take any excuse to break into other molecular arrangements. It takes very little kinetic energy to make the whole mess fly apart.

ammonium tri-iodide is the stuff they often make in chemistry classes isnt it?... well or often made twenty years ago.

If so, or if not apply this anecdote to whatever that explosive is, one hilarious property it has is that it is made in some sort of wet solution, then as it dries it becomes less and less stable. This causes chemistry teachers to do stuff like whip up a small batch, set some of it off for the students, and throw away the bits of paper they dried the stuff out on. This paper usually has small specks of the stuff still on it, and it sits in the wastebasket drying out. Hours later somone tosses something into the trash, or tries to empty it, or walks past it and there is another small but very startling explosion. This property is also supposed to be great for practical jokes, you smear it on some humorous surface (say the underside of a chair) and hours later somone just touches that object and it goes off.