"By increasing the number of dangerously exposed sawblades in the workplace, you can terrify your mill-workers into higher rates of production and efficiency. With Advanced Lumber Mills, you can get twice as much Lumber per day out of the same number of workers!"
Lumber Mills turn your stockpile of Wood into Lumber. The Advanced Lumber Mill obviously does this at a higher rate of production. Lumber isn't as required of a resource when compared to Concrete or Steel, but players will want to keep their reserves full and plentiful, especially if they plan on promoting Critter units, such as the Battle Raptor or Imperial Boar, or upgrading buildings to very high levels.
Refer to the Lumber Mill for more information on how Lumber is used.