Axes are used to cut wood faster then anything else. Wooden axes are a little bit faster then hand but not much. Here are the axes from strongest to weakest.

Axe durability:

Golden axe: 33 uses

Wooden axe: 60 uses

Stone axe: 132 uses

Iron axe: 251 uses

Diamond axe: 1,562 uses

Wooden axe: like I said, a little faster then by hand

Stone axe: after using wood, this thing mines fast

Iron axe: same iron quality good

Diamond axe: bet you didn't see expect diamonds in second place. Mines faster then a second.

Gold axe: it may break quicker, but gold axes mine the fastest

Here are the enchantments:

Efficiency: mines faster

Unbreaking: more durability

Fortune: drops extra blocks

Axes are the second strongest weapon to fight with, so if you don't have a sword, use a axe.