Food is fuel, and backcountry adventures burn a lot of it. You can get calories laminated in many forms to be eaten with one hand on the go, but that can be anticlimactic against the background of an epic vista or a new entry in your trail log. Hot meals improve attitude, provide a social setting, and, of course, warm you up. But you can't prepare it without a stove.
Backpacking food is dehydrated, prepackaged, and remarkably tasty, in small doses (anything gets boring after the fourth week on the same menu). But you don't 'cook' it, you rehydrate it. The primary function of a backpacking stove is to boil water, and this affects the overall design and feature comparisons when you're shopping.
Developed using the same concept as the blowtorch (and later, cigarette lighters), the modern liquid-fuel backpacking stove design was introduced around 1892 and used with great success by the Amundsen, Mallory, and Byrd expeditions to the poles and Everest. They found the light weight and efficiency critical to survival in an age before emergency beacons, heli-rescue, and satellite phones. Some models of Primus and Trangia stoves are unchanged in design, and all liquid-fuel stoves use the same principles as those pioneers.
Liquid fuel is pressurized in the tank, which moves it into the burner assembly where it is heated and vaporized, then burns as it exits via the jet nozzle. Flame intensity is adjusted with valves at the tank and burner assembly. The fuel is some form of gasoline or diesel fuel, preferably 'white gas' which is highly refined gasoline, without many of the additives of commercial fuels. Some stoves are designed to use white gas exclusively, while 'international' or 'multifuel' stoves can burn a wider range, though with lower efficiency. Adventures beyond your usual haunts have many variables, and
The details of using a liquid-fuel stove will vary by manufacturer but follow this general outline: Pressurize the fuel in the bottle, connect to the burner and fill the priming cup with a small amount (1/2 teaspoon) of fuel. Light it to warm the generator tube, so as fuel passes from the bottle to the stove, it is heated and vaporized. After a minute or two, the priming flame will die down. Open the flame control valve to start the flow of fuel, and the priming flame will light the stove. Adjust flame to the minimum needed to get your heating done.
Canister stoves use a compressed fuel vessel containing a blend of propane and butane. While the canisters have a standardized 'Lindal' threaded valve connection, each brand claims that only their fuel will deliver the claimed performance. Using a canister stove is very simple, basically 'turn it on and light it,' as if your gas stove at home had no pilot light. This convenience means less time getting dinner started and more getting other things done, like airing out your socks. They are much lighter, simpler, and less expensive than liquid fuel models, but cannot be adjusted for altitude and temperature variations, and can be difficult to track fuel usage. The empty canisters can be recycled, but cannot be crushed to conserve space for packing out.
The weights and dimensions listed by the manufacturer will be pretty reliable, but remember that they never include fuel. Boil Time can be a bit tricky, however, because in the end it's not really a valid specification. When shopping for cars, how important is 0-to-60? If the stove is on at full flame, the efficeincy is very low and while you may gain time, you are losing fuel. The same goes for Burn Time, since keeping the flame low means it will run longer. The manufacturer won't use invented numbers, but remember that Your Mileage May Vary.
Like many pieces of backpacking gear, over the course of many trips and adventures, you may end up owning more than one stove. The major decision between liquid and canister fuel is better thought of as 'light 'n easy' versus 'durable and future-proof.' If your trip is relatively short with little cooking, a pocket-sized stove and single small fuel canister will save weight and time. If, however, you are traveling where you can find gas stations but not gear shops, an 'international' model liquid stove can be refueled easily and you'll know how close to are to needing more. Canister stoves tend to have small pot stands and are not as stable as bigger liquid fuel models, so if you prefer one stove for five people, that big pot will be right at home on a wide, low burner.
In any case, the stoves are designed to last several lifetimes, with very few moving parts and easy maintenance. Don't abuse it, and you might pass the stove on to a newbie somewhere down the trail.