Although cooking over a campfire is a classic and very enjoyable way of preparing your meals in the outdoors, there are many situations where it simply isn't possible. Lack of firewood, burn bans, high altitude, wet environments... the list goes on. For all of these situations, and for a quick and reliable method, camp stoves are your go-to item.
Liquid fuel offers excellent cold weather operations, numerous inexpensive fuel options, the ability to take only the fuel you need, reusable containers, and generally a more stable cooking base. However, these stoves are more prone to leaking, are a bit heavier, and require priming.
Another thing to note with liquid fuel stoves is the availability of kerosene internationally as an easy fuel source, so these work out better for the international traveller.