"Lying in the middle of the path is a perfectly good axe head. Apparently, the owner discarded it when the handle broke. But you simply carve a new one from a solid tree branch, test it with a few swings and tuck your new Axe in your belt."
—When the Axe is picked up
It provides a generous attack bonus, and it's an useful item to have, even though it decrease their movement. It was reported that the description is bugged and that the Axe actually provides only +7 Melee Attack to the hero, but this is not true.
Like all basic items, the Axe is useful, but only before better artifacts can be obtained.