Forests are where wood is gathered. Lumbering Camps are built next to forests in order to do so.
Each forest only contains a certain amount of wood, and will become depleted from gathering. New forests spawn on the map at around the same rate that forests are depleted, so there is never any real shortage, although at times it may become harder to find forests, especially if you are in a very populated area of the map. There is a bonus to the rate of gathering if more than one Lumbering Camp is working at the same forest. Each player can only place one camp at each forest. A city may have up to 5 Lumbering Camps active at a time, although the total laborers at those camps is determined by that city's Lumbermill level
The rate at which your camp produces wood is approximated by Laborers * Rate * CampBonus where the Rate is 0.75 for Lumbermill levels 1-2, 1.00 for Lumbermill levels 3-6, 1.25 for Lumbermill levels 7-11, 1.50 for Lumbermill levels 12-15, and the CampBonus is 1 + 10% per camp. See herefor data. This is an approximation only, the actual formula is unknown.