http://en.wikipedia.org/wiki/Meal,_Ready-to-Eat
And the changing menus http://www.mreinfo.com/us/mre/mre-menus.html
The whole thing comes in thick plastic bag. When you cut it open you get several plastic bags and small cardboard boxes. The flameless heater is just another empty looking plastic bag (lower left in the picture). Inside the boxes are the main parts of the meal inside of sealed tin lined bags (think of them like a flexible can) -- I think the food is pasteurized for long shelf-life.
To heat up the food, you put a little water in the heater bag and close it up. You then put one of the courses and the heater bag together into one of the cardboard boxes and the reaction will kick in in a sec and make the heater bag really hot. You wait a couple minutes while it heats up the food and then you can take it out and eat a hot meal. If there are two courses you can then repeat (the heater bag will stay hot for quite a while). Or you can try and heat up some water for instant coffee.
Most of the meals also come with a little salt/pepper and Tabasco sauce so you can season to taste (which really helps with the omelet meal which I think they got rid of).
Most everything else is designed not to need heating, it's like crackers and peanut butter or something else. There's usually a sports/electrolyte drink or some kind of drink mix fortified with vitamins and such.
One thing that the military is really proud of is that these things have like a 3 year shelf life without the use of preservatives.
You can actually buy civilian versions (without the heater) http://www.mreinfo.com/civilian/mre/civilian-mres.html
Also, they seem to include the heater these days: http://www.mreinfo.com/civilian/mre/civilian-mre-comparison....