According to the UNESCO world heritage site management plan Białowieża Forest is divided into four zones, with an additional buffer zone around the outside. These are as marked in the key on the map above. To cut a long story short, the management plant prohibits forestry in zones 1-3. Zone four is where forestry is permitted, to provide the local population with a supply of wood.
The UNESCO management plan is legally binding due to Poland signing the UNESCO charter in 1946. Article 87 of Poland’s constitution enshrines international agreements within Polish domestic law.