The Battle Axe was a weapon for sale by the Weirdling Tradesman. A finer battle axe is not to be found. Indeed, one's foes tremble at the mere sight of it! The tradesman offered it for 500 gold coins and the trade-in of Connor's used weapon, if he so chose to buy it.
It is a rather expensive weapon, and will be replaced soon enough with better. So its best to ignore it.
In the KQ8 Hintbook its called the 'battle-ax'. Its suggested that Connor may have bought one (or rather recommends buying one, if if the player has money).