A fire axe is an axe designed to help fight fires.
While Sam and Dean were rescuing their father, a demon-possessed fireman bursts into the apartment with a fire axe.
While under the control of the Siren, Dean tries to kill Sam with a fire axe. However, Bobby Singer intervenes, stops Dean from killing Sam and kills the Siren, breaking its hold over the Winchesters.
When facing Leviathan Sam and Leviathan Dean, Dean Winchester arms himself with a fire axe. After Sheriff Osborne splashes Leviathan Sam with borax, Dean uses the axe to decapitate him. Dean then splashes his Leviathan counterpart with borax and decapitates him with the fire axe.
During the Battle of Linwood Memorial Hospital, the Farmer Angel arms himself with a fire axe to break through the door to Sam Winchester's hospital room. The blows from the fire axe begins breaking the angel warding Dean placed on the door to protect Sam from the attacking angels. Dean is eventually able to use an angel banishing sigil to banish the Farmer Angel and the Kim Schortz Angel before they can finish breaking through the door. It is unknown what happened to the axe when the angel holding it was banished, but it appeared to disappear with him.