First off, before there was Jubilee, and Angel, and every "whatsits" character with porcupine quills popping out of their face, there were founding members of the X-Men: Charles Xavier and Jean Grey to name a very short list. Chris Claremont (who was a writer in the mid 70's) gave Jean Grey some greatly enhanced abilities. As a result, Jean Grey was far more powerful than anyone else on the team of X-people. If you haven't noticed, boys and guys who are nerds (this is a broad realization but it's true...please believe me) like hot chicks that can fight. Yes...it's a thing. They don't like Audrey Hepburn "elegant lady" types. They want (and have for decades) liked tough talking hot babes (who still shave their armpits and legs) but who know how to take a punch in high heels (Wonder Woman) while being "edgy" (Netflix Jessica Jones or a young Jessica Alba). Bonus points if the heroine has red hair. Yes...this is a thing. Please don't shoot the messenger. Call it a fetish if that makes any more sense. Nerds are just narcissists that haven't discovered "edgy" yet.
As a result of the increased power and the fact that Jean Grey fit all the stereotypes named above, she was a popular character. And adding to all of that power was the underlying mystery of where it was coming from. Claremont (to his brilliance) seeded the story run with hints that Jean's growing power was corrupting her. She was kind of falling under the influence of a malevolent entity. "The Dark Phoenix saga" is a chronicle of all of that drama. And for you writers out there, I also want to mention that the writing in this particular series was as solid as they come, the stakes were very high, and Jean Grey perished (which at the time was significant because comic book deaths were still a kind of novelty). So all of those things just fed into why this tale was so epic.
The drawing in these issues was incredible too. There was a George Perez-like attention to detail with every panel strewn with things that you just don't see in today's comic books. The story arc had no tie-ins either. It was nine issues with an extra large conclusion. Characters who are popular X-Men today made their first appearances in these issues and the Scott and Jean relationship is (of course) central to everything. Because of the Dark Phoenix saga, Scott (Cyclops) is haunted for years.
So yeah...The Dark Phoenix Saga was (and is) a big deal. I wonder if one movie is going to do it justice. My guess is...probably not. But when it eventually comes out, I'll see it anyway. There's so much good story there to mine that it seems like it would be impossible to mess up.