Logging Skill is a skill that involves cutting Trees.
You can also cut saplings, which are cut down more easily but give less items. Only saplings in the before last stage of their growth (when they look like mini trees) will drop items.
If a tree is cut and falls into water, you'll have to watch the items from the tree appear, then fall into the water with a splash.
Lulu Lopez will comment on your logging, and tell you to plant more trees if you cut down too many. Trees can only be planted in your Manor's garden.
Trees will fall either left or right depending on where the player is positioned when they cut down the tree. To the right is a grid showing the tree fall direction based on where the player is logging from in a 3x3 grid. (T= Tree, R = fall right, L = fall left).