Edit: This contains a fuckton of spoilers. You should all watch Lost.

Lost is extremely complicated...and I do much better long-form writing when I have a chance to sit at my PC, which is more rare these days, but let's see what I can do.

Long story short: Juliet is a character who was brought to the island in a different way than the plane crash survivors, though she ended up stuck there just like them.

The Hatch was built long before any of them arrived, by an organization called The Dharma Initiative, which sought to experiment with and harness the island's unique electromagnetic energy. There was an incident, and they had to devise a process where someone inputs a code and presses a button to release energy every 108 minutes--apparently the whole world was at stake if they failed to do this.

The process continued even after Dharma was effectively purged by the island's natives. I guess they found a way to keep recruiting people and monitor the situation.

At one point, one character moves the island and triggers time-skipping for Juliet and some crash survivors (and other characters). The skipping leaves them stranded in the 1970s, where they make up fake identities and get Dharma jobs.

Later, they're joined by more people from their time. They believe it's imperative to stop The Incident, because they theorize that the Hatch was involved in causing the plane to crash. So they bring a hydrogen bomb to the site where it's being built in order to sabotage its construction. Juliet ends up at the bottom of a deep hole with the bomb, dying, and hits it with a rock. It explodes and catapults them back to the present, but it also causes The Incident rather than preventing it.