What a coincidence that you and Gordon are reading the same book and have exactly the same question! The Natural History of Selborne was written in 1789, so one must be aware that the English language used in this book is over 224 years old. The older meaning of words, and/or their meaning specific to southern England, must be taken into consideration. "Hanging Wood" is probably an area on a cliff covered by a growth of trees. To the observer, the trees growing off the side of a cliff would look like "hanging" trees, hence the name "Hanger."