Although the Parting the Veil quest started alongside Season of the Deep, it’s an extension of the Destiny 2: Lightfall storyline. When you complete this quest, a Lightfall campaign marker will pop up in the Veil Containment area of Neomuna. Enter the mission to find the secret audio logs explaining the Veil.

During the Parting the Veil quest, a glowing computer screen above the Veil shares a personal audio log of Chioma Esi, an Ishtar Collective researcher and one of Neomuna’s founders. After you complete the quest, revisit this computer to access audio logs explaining Esi’s and Maya Sundaresh’s studies of the Veil, the Vex, and the murky history of Neomuna. Keep in mind, you can’t access the Veil Containment audio logs by patrolling Neomuna; use the Veil Containment marker on the map instead.
The Parting the Veil final mission reiterates bits of lore from the Lightfall campaign and the Root of Nightmares raid — like Nezarec disclosing that Savathun brought the Veil to Neptune, for example — but the research and incident logs that come after are revelatory.
The Parting the Veil’s final mission had an inconclusive ending — with Osiris saying that he needs several days to break through Esi’s encrypted logs protected by a Vex algorithm. The decrypted archive audio logs in the Veil Containment are likely part of Osiris’s decryption process.
Since the start of Season of the Deep, the Veil Containment mission has shared a new audio log each week, although, for now, it’s unclear where this lore leads (and how many audio logs there are).
Besides explaining the purpose of the Veil in Destiny 2, this short quest rewards you with the new Legendary masterworked Epochal Integration hand cannon and a new Strand Aspect.