As well as the tannins mentioned above, some wood can slightly acidify the water over time. These include Bogwood or Mopani wood, which can be beneficial for species that thrive in lower pH environments.
Aquarium wood can affect the general hardness (GH) and carbonate hardness (KH) of the water by releasing certain ions, but this effect is usually minimal compared to its effect on pH.
Wood surfaces can also house beneficial bacteria that help in the nitrogen cycle, particularly in breaking down waste products which helps to create a healthier aquatic environment.