Game Info
Terrain feature found on tundra, plains and grassland tiles.
- Base yield: 1
Food Food, 1 Production Production
When cut down, provides a lump sum of 
Production Production to the nearest city of the Worker's civilization. Provides +1 bonus 
Faith Faith if unimproved and next to a Celtic city (+2 bonus Faith Faith with 3 or more unimproved tiles).
Strategy
Forests present interesting opportunities, such as some unique resources like Deer and Truffles, and a natural defensive bonus. They also provide a one-time boost to a nearby city's Production Production process when cut down, which can be used strategically. Lumber Mills, Camps, and Trading Posts can be constructed in forests without cutting them down, but ordering any other tile improvements will cause them to be removed (still providing the one-time production boost).
Forests in tundra terrain are very important, because they effectively improve the base terrain yield, so try to preserve them there should you settle a city in the tundras. Also, the Iroquois and Celtic civilizations have unique bonuses and buildings which make a very effective use of Forests - when playing with them, search out and settle in or near forests.
Civilopedia entry
For early man, the forests were a great source of bounty, providing wood for fire, tools and shelter, and also many animals for sustenance and clothing. As a city grows there is a great temptation to cut down the forests for farmland, but a wise leader will always leave some standing - for productivity and to lift his people's spirits. Also, military units stationed in forests receive a significant defensive bonus.