First and foremost, she is Ultimecia's main objective for venturing into the past. The sorceress seeks to get ahold of her so that she can use her time magic to carry out time compression. The result of this is the numerous battles with possessed sorceresses that Squall must fight during the game.

Indirectly, Ellone is the reason why it is even possible for Ultimecia to send herself into the past. The machine that Ultimecia uses to do this was originally constructed using information attained from the study of Ellone's brainwaves. If Ellone had not been alive, or had she not had her powers, then the machine could not have been created, and Ultimecia would have had no way to go to the past.

Thus Ellone is the root of the problem which must be overcome.

Don't beat up on her yet, however, as she is also a part of the solution. Using her time magic, Ellone sends Squall and his party far into the future, a world in which time compression has already been attained. It is there that they are able to fight and defeat Sorceress Ultimecia, eliminating the chance of her causing anymore problems for them in the future.

So basically, without Ellone there would be no storyline. Ultimecia would not be bothering them and they would not have to defeat her. What a boring game that would be!

Ellone is also a huge factor in the emotional story of the game. It is because of her leaving that the protaganist, Squall, becomes so cold and detached from the people around him. She is the reason for his constant state of emotional anguish, and sets the scene for Rinoa's entrance into his life. If he had never known Ellone in the first place, he would not have had to experience losing her and would never have had to learn how to love again. Without her presence, the emotional growth and development that he experiences through out the duration of the game would be for naught.