Greek Fire provides a +40% increase over the normal range of 2.49 that Fire Ships normally have, allowing Byzantine Fire Ships, already the best in the game, to fire from much further away. Not only does it make Fire Ships even more effective against Galleons (in some cases they are able to take out large masses with proper back-up), but it also allows them to raze significantly more shoreline infrastructure, something Cannon Galleons can have trouble with in some cases. Also, the Fire Ships' combat capability in shallows against land units greatly benefits from Greek Fire.
In reality, the naval weapon known as Greek fire, or "liquid fire" was a substance of unclear composition that burns intensely when projected even when doused in water. Based on historical records, it is used in liquid/sludge form and was notably dense, therefore having a very low effective range (Greek fire is most commonly poured directly onto an enemy ship's deck during a clash), thus the range improvement as depicted in the game is somewhat erroneous.