A wood furnace is a specialized form of furnace designed to burn fresh wood. Unlike the other non-magma furnaces, a wood furnace does not require fuel to operate.
Any dwarf with the wood burner labor enabled can burn a single log in order to produce either ash or charcoal. While it's hardly efficient, charcoal serves as the most ubiquitous form of fuel available to run a metal industry on. Ash sees use in multiple industries, such as glazing earthenware items, advanced glassmaking, crop fertilization, and soap production. As with all buildings that require an architect, passing dwarfs may admire wood furnaces and receive a good thought.
Wood furnaces can be built from any fire-safe material. Once you designate a spot for your wood furnace to be built, a building designer will bring the material to the site and design the building before the actual mason (for stone or glass furnaces) or metalworker (for metal furnaces) comes along and builds it. Strangely enough, charcoal and coke are valid mason's materials for building a wood furnace, since their ignition point is above the cutoff for fire safety. A carpenter will be necessary if you choose to make a literal wood furnace out of the one fire-safe wood, nether-cap.
The overall value of the wood furnace building helps determine the strength of the good thought dwarfs receive when admiring it. This value is determined by both the value of the material used in its construction, as well as the quality of both the architect's and builder's efforts.
 Minimalist start
For players trying to maximize the value of their embark points, you may wish to avoid bringing finished battle axes or picks, choosing instead to bring metal ore and fuel with you, so you can forge them yourself. Including a wood furnace can be extremely useful here, allowing you to turn logs into fuel much more cheaply than bringing coke, while bars of ash are inexplicably magma-safe building "materials."