Fires provide warmth to prevent players from freezing. In the Forest and Ocean, players get cold slowly at day and quickly during the night. In the Winter, heat loss is extremely fast in both the day and the night. Once the heat bar is empty, every tick chips off some of the health bar, making fires necessary for survival.
It is advised to not stay too close to the centre of the flame when using a campfire or the big fire, or the player will start taking damage (20% of life bar every 5 seconds), which is not very noticeable and can kill the player.
The Campfire is the lowest tier fire. It can easily be crafted with 25 wood and 5 stone. It burns out (disappears) after 2 minutes (half of a day or night). Campfires are also used to craft Big Fires.
The Big Fire is the highest tier fire, lasting 3 times as long as the Campfire. Since Big Fires are crafted with 35 wood, 10 stone and 1 campfire, it is more efficient in terms of resources than the Campfire, costing 15 less wood than the equivalent 3 campfires. Big Fires, if placed at the start of the night, will last until the middle of the day.
The furnace is a reusable fire that behaves like a one-way-chest, as players can put any amount of wood into its inventory, but can not take any out. As long as the Furnace contains at least 1 wood, it will give out heat. However, 1 wood will "burn" every 6 seconds, and disappears from the furnace's inventory. Unlike other fires, it is impossible to take damage from a furnace (as the heat is contained). It can also act as a wall, being a solid structure incapable of being walked over.
For each night, around 40 wood gets used as fuel in the furnace (the night lasts 4 minutes). Try not to dump in all of the wood, or it will most likely get wasted during daytime. When AFK, make sure that you are in the range of a furnace.