Can be used in very early levels to kill on its own. In higher levels it can soften enemies to be more easily killed with a more powerful CA.
The Licking Flames and Hunger modifications can cause a wildifre that spreads very far very fast. The Community Patch nerfs these values as they can make Eternal Fire bring down multiplayer servers. Viperish Disease was nerfed in much the same way, and for the same reasons (see that page for further explanation).
Eternal Fire should usually go near the beginning of a combo so that it has time to spread to as many enemies as possible.
Pros and Cons
Can spread very far very fast.
The only thing that increases the damage is the CA level. No skills or item mods affect the power of Eternal Fire.
Very weak increases in power as the level increases.
Eternal Fire inflicts a special type of damage (called "Plague Fire" in the game files) that is neither normal Fire damage nor Fire DoT, despite the word "fire" in the CA description. Therefore it is not boosted by +Damage modifiers and is not resisted by Armor.