Woodcutting is a gathering skill that primarily involves chopping trees to obtain logs used in the Fletching, Firemaking, and Construction skills. Players with a higher Woodcutting level can chop down new types of trees and cut down trees quicker. As levels increase, players can use better axes to chop trees faster. Players with high enough Attack levels can equip the axes that match the respective metals, but you don't need to equip an axe to use it to cut down a tree. Having it in your inventory will suffice.
Woodcutting is a useful skill for a low-leveled player to make money early in the game.