Eye of Fire is a very rare item only dropped by killing a Dynonn. Its uses make it very valuable. A villager in a black robe will trade an Eye of Fire for 64 Emeralds. It randomly ignites blocks on fire around the player when in inventory. It is one of the four items needed to craft an Inferno Staff.
Right-clicking an Eye of Fire on a Dynonn will make the Nether mob transform into a Nightmare Dynonn. Or, they can be used to find nearby Nether Fortresses and will blink red faster when there are blazes in a 40 block range.