Lost is, in essence, Survivor meets Cast Away, except with a smoke monster. Oceanic flight 815 departs Sydney, bound for Los Angeles, and crashes a thousand miles off course on a mysterious island in the south Pacific. The survivors quickly realize that help isn't coming and have to figure out how to survive life on the island and avoid the polar bears in the jungle. That, and they're not the only ones on the island.
Juliet is introduced in season 3 as an Other, one of the people who was already on the island before the crash. She comes in conflict with the survivors as she tries to urge them to help the Others' leader with something he desperately needs — but Juliet has her own agenda, and what she wants isn't necessarily in line with the Others.
Over the course of the show, Juliet is one of the best characters to watch develop — she starts out as an antagonist, but like everyone on the island, she's got a backstory to explain just how she got there, and where she ends up is quite different from where she began.
Getting into any further detail would drop us into spoiler territory, so instead I'll encourage you to check out Lost if you managed to miss it while it was airing. Fair warning, though: make sure you've got a lot of time. It's a damn hard show to put down once you start.