WARNING: The following contains spoilers for Loki Episode 1, "Glorious Purpose," streaming now on Disney+.
The term "Nexus" was first introduced to the Marvel Cinematic Universe in WandaVision Episode 7 as the name of an antidepressant in a fake commercial. The commercial's narration claimed this drug "works to anchor you back to your reality -- or the reality of your choice," possibly foreshadowing a multiverse-based story arc for Phase 4. While the term didn't come up again in WandaVision, the series premiere of Loki defines what Nexus actually means within the MCU.
As explained in Miss Minutes' animated orientation video for the Time Variance Authority, a Nexus Event is any event that causes someone to stray from the Sacred Timeline created by the Time-Keepers. A Nexus Event can be as seemingly minor as showing up late to work or as dramatic as stealing the Tesseract to escape justice for attempting to conquer Earth, but whatever these events may be, the TVA does not approve.
The Time-Keepers are three ancient beings who lived through a multiversal war. They created the Sacred Timeline in order to prevent the existence of a multiverse and stop a multiversal war from happening again. The TVA exists as a means of maintaining that timeline and punishing "variants" -- those whose actions have caused Nexus Events. As of the end of Loki Episode 1, the Avengers: Endgame-created variant of the God of Mischief has been given the opportunity to make good by hunting down even more dangerous variants of himself on behalf of the TVA.
This is, in essence, a more detailed explanation of the concept of branching timelines and the need to correct them previously introduced in Endgame. The major uncorrected timeline divergences created by the Avengers' time travel adventure -- Loki's escape in 2012, Thanos leaping from 2014 to 2023, Steve Rogers deciding to spend a lifetime with Peggy Carter -- might be considered Nexus Events. It's unknown how the TVA handled the Thanos situation, but a background Easter egg in Loki Episode 1 could suggest that the TVA is punishing Peggy for Steve's actions. Loki's trial makes it seem like the Avengers are treated above ordinary cosmic law because their actions are already part of the Sacred Timeline.
A multiverse is coming to the MCU, whether the TVA approves of it or not. Spider-Man: No Way Home is said to build on the hints introduced in WandaVision, and it's right there in the title of Doctor Strange in the Multiverse of Madness. With all the potential Nexus Events on the horizon, it looks like the officers of the TVA are going to have their work cut out for them.
Loki stars Tom Hiddleston as Loki, Owen Wilson as Mobius M. Mobius, Gugu Mbatha-Raw as Ravonna Lexus Renslayer, Wunmi Mosaku as Hunter B-15 and Sophia Di Martino, Richard E. Grant, Sasha Lane and Eugene Cordero. New episodes stream Wednesdays on Disney+.