Basically in Pre-Sequel you help Jack rise to power and fulfill his mad dream of opening the Elpis vault. The vault of The Sentinel and Empyrian Sentinel...they were a challenge in their own way. But this is about Jack, who, after the vault was opened and the Sentinel's defeated, became scarred with the ever so popular vault symbol after Lilith destroyed the relic.

Then came the story of Borderlands 2, which was released before The Pre-Sequel. Jack at this point had taken over the Hyperion Corperation and was determined to locate the Pandora vault that contained The Warrior. He had taken to calling himself Handsome Jack. Basically at the end of Borderlands 2 you have to defeat Jack and then The Warrior, you can then either execute Jack yourself, or let Lilith do it.

For more, here.