Once the Sunfire was enshrined in the Kashuan Keep, the people needed a way to actually carry it. As such, Egil's Torch was made, and it was the only thing capable of carrying the Sunfire. However, the King knew that people would want the torch and fire, and so built a door into the Keep that needed one of three keys to enter. A Red Soul was also charged with guarding the torch.
The torch is also used in a ceremony every three years. The torch is lit, to ensure that the Sunfire will keep burning and never go out.
While not actually appearing in the game, Egil's Torch is mentioned in a Mognet quiz where the player is required to put three events from Final Fantasy II in order. One of these is obtaining Egil's Torch.