Woods increase the base yield of a tile by +1 Production. Woods raise the Appeal of surrounding tiles by +1, and increase the combat strength of defending units by +3 . Woods also provide +0.5 Faith to adjacent Holy Site districts (rounded down).
Once the Conservation civic has been unlocked, Builders gain the ability to plant Woods on appropriate tiles. "New-growth woods" (that is, woods planted by Builders) provide the standard +1 Appeal bonus, while the appeal bonus of "Old-growth woods" increases to +2.
Woods have many uses throughout the game. Forests ensure productivity and protection for civilizations living within them, and provide adjacency bonuses to Holy Sites. Once Machinery is researched, Lumber Mills can be built to increase their Production (especially along rivers).
In contrast to Rainforests, Woods will increase the Appeal of nearby tiles, making them ideal for Neighborhoods or tourist attractions. The Conservation technology also allows workers to plant New-growth Woods; while they don't have as much appeal as Old-growth Woods, they can be used to dress up cities and improve tiles in tundra environments.
The bounty of woods has been crucial in the survival of more than one tribe, providing timber, animals, and plants in such variety as to stagger the imagination. Sadly, civilization has too often chopped them down to make room for farms, roads, and suburbs … and then there are those greedy corporations, looking to grow rich from pelts, logs, and metals.