From Destinypedia, the Destiny wiki
Expunge were a series of missions released during Season of the Splicer. They served as one of the primary storytelling methods for the season. The missions follow The Guardian and Mithrax, Kell of Light as they navigate through the Vex network and unravel the forces sustaining the Endless Night. There are four missions total, with three "Corrupted" versions of the missions. In order to access Expunge, players would need to complete the weekly seasonal quest, unlocking a new mission each week. Expunge was made to be no longer available upon the release of The Witch Queen expansion.
All Expunge missions begin the same. Players will spawn in the Vex network and proceed forwards. Here, they will drop down and navigate through a series of constantly changing Vex code that attempts to stop or crush any players that are not careful. After making their way past the code, players will be encountered with a large jump into a hallway. Just like before, players must proceed forwards with the shifting landscape blocking passageways and attempting to crush players. However, players must be quick as a Vex firewall will begin to advance forwards. Touching this red wall will instantly kill a player. The firewall is easily detected as it makes a loud sound when close by. Along the hallway, there are a few crevices that players can take refuge in and allow the wall to pass ahead of them. When the firewall reaches the end of the hallway, it will reset at the beginning and begin to move forwards. If the player had bought the "Wirewalker" upgrade at the House of Light's Servitor, a shortcut will bring players straight to the Vex firewall section. After passing the firewall, players will then be teleported into their next section.
Expunge: Labyrinth is a large parkour and platforming puzzle. Players will make their way across an open chasm, jumping on appearing Vex platforms and defeating Vex forces, including Barrier Hobgoblins. Occasionally, players will need to defeat a Nexus Guardian and carry their Data Spike into a terminal to move forwards. Players are done with this section when they encounter a large, flat platform. Players will jump the gap to begin a boss fight with Fantis, Oppressive Mind which is a large Minotaur. When the fight begins, players will be able to damage Fantis but they will soon pull up a shield to defend themselves. Players will need to find and destroy Nexus Guardians and ride the Vex launchers to deposit their Data Spikes into Terminals. When three Data Spikes are deposited, the shield will drop and players will be able to damage Fantis again. If players do not defeat Fantis within the allotted time, Fantis will pull up another shield and players will repeat until Fantis is destroyed.
Corrupted Expunge is a harder difficulty version of "Expunge: Labyrinth," "Expunge: Styx," and "Expunge: Tartarus." "Expunge: Delphi" did not have a corrupted version. Players needed to acquire Corrupted Key Codes to access this mode, which had stronger enemies, more Champions and replaced most enemies with Taken variants.