Axes is a classification of tools known in vanilla Minecraft to be used for gathering wood. Tinkers' Construct adds additional Axes that can be crafted various materials and put together at a Tool Station or Tool Forge. Harken Scythe, Twilight Forest, Falling Meteors and Better Dungeons also add new types of Axes.
Tinkers' Construct Edit
The Axes do not need to be made of a single type of material and can instead be mixed and matched with each other to provide fairly unique Axes. These Axes can then be modified using a Tinkers' Construct Tool Station or Tool Forge with the appropriate modifiers to permit for various additions to the tools that may otherwise be impossible to achieve in vanilla Minecraft.
The list of possible materials, in no particular order, axes can be made out of are:
Harken Scythe Edit
Twilight Forest Edit
Falling Meteors Edit