Trioxane is a compressed, solid fuel, used for cooking food, boiling water, or heating MRE's, otherwise known as military rations. They were made mainly for survival and military use and usually come packaged 3 bars to a box. Each bar is individually sealed in a coated, water proof, foil wrapper and every bar is scored so that you can break it into thirds to vary the amount of fuel burned. There's nothing to spill and they are reasonably lightweight.
Except in the exact chemical makeup and burn times, they are pretty similiar in use to esbit tablets. One bar will burn for about 7 to 9 minutes at over 14,000 BTUs, which is plenty long enough to bring a small amount of water to a boil. They burn so hot that you will probably only need to use one full bar to make a good cup of java.
Designed for outdoor use, (not for use inside a tent), Trioxane is (very) easy to light, and can be used in a variety of ways. They can be used in an esbit type of stove, in a specially designed trioxane stove, or if you have nothing else, simply place one on dry dirt or a rock, and hold your pot or canteen cup over the flame for cooking. I've used them in emtpy cans, and in my sterno stove in the past. As with most fuels, when cooking with trioxane be sure to allow the fire enough ventilation to breath, but you will probably need to protect the flame from the wind.
One drawback to using this type of fuel is that there isn't any real practical way to vary the heat intensity. Once you ignite the fuel bar there's only one real heat setting - High. The only practical way to vary the heat that I've found so far is by varying the distance between the fuel and the cooking pot. This of course can be easier said than done when out in the backcountry or on a trail somewhere.
They do leave a little residue after burning and the instructions indicate that you should wash your hands if your skin comes into direct contact with the tablets. Personally, I take that to mean that they are probably somewhat toxic. They seem to have a slightly toxic smell when burning so I would suggest that you try to avoid inhaling the fumes while cooking if you can.
As mentioned earlier, they are really made more for survival type of cooking. They are best at heating or boiling small amounts of water (for a single person. A task at which they seem to work rather well at, but probably not much else. I haven't actually tried to cook anything with them, but they seem too hot for anything else but boiling water to me. The advantages to this type of fuel is that they are extremely lightweight, there's no liquid fuel to spill, and there's nothing mechanical that can malfunction.
For backpacking purposes they can be usefull if you mainly rely on dehydrated foods that only require boiling water for a few minutes, or making coffee or tea. In other words if you are a minimalist, or an ultra-light hiker, then they will probably get the job done. If not, then they should be used more for a backup fuel source, as opposed to using them as your main source of cooking fuel. At the very least, I would suggest that you try them out on a one or two day trip to see if you like them before heading out on any longer excursions.