This tool will cut down just trees from the area that you select - and leave all other resources on the ground. Each full-size tree will be converted into 3 logs, whereas smaller growing trees will give proportionally less wood.
This tool is by far the best way to get wood for building at the start of the game, but eventually you will run out of nearby trees, and have to start building forester lodges or importing logs from a trading post.
If you urgently require additional trees, using this tools in the vicinity of a foresters lodge can give you a temporary boost, at the expense of fewer trees for the next few years.