Unlit Bronze fire arrows are used during the Underground Pass quest. They are created by using a damp cloth on regular bronze arrows. The arrows can be lit by using them on a fire to create lit bronze fire arrows. The lit fire arrows can pierce the rope in the Underground Pass Dungeon to lower the bridge. This is necessary to complete the quest.
Bronze fire arrows have the same Ranged Strength bonus as regular bronze arrows, and the fire provides no additional benefit.