Desync, simply put, is when an online game server and client don't agree on a player's location: The client says a player is here, but the server says they're actually over there. As you can imagine, it's a real problem when you're trying to put bullets or blades into someone, and it's been an issue in Halo Infiinite since before the game released.
"Usually, the moment we detect a desync, no matter how small, the client should begin correcting to the server’s position. In bad cases this results in rubberbanding, but in normal scenarios these changes should be unnoticeable. The cases where you permanently desync occur when our systems fail to detect and respond to desyncs."
343 said at the time that it had identified multiple situations in which Halo Infinite players could become permanently desynced, and expected to have a fix "deployed in upcoming builds." But the problem has persisted, and it sounds like it's going to be around for awhile yet, as developers' hands are currently full with other things.
"I don't know if twitter/reddit is the best place to go into all the details about why there's been a lack of UCN [networking] improvement, there's a lot of factors, so I'll keep it brief," 343_Taxi wrote in response to a video illustrating desync problems that was posted earlier this week. "The TLDR of it is the devs that would work on these fixes have been allocated to other Infinite work. Their work has had some knock-on benefit to our UCN solution, especially around movers (players, vehicles, etc.) on object devices (elevators, pistons, bridges etc.), but not around the melee and 'around the wall' shots. These devs are coming home to Sandbox soon (hopefully).
"The Community and Competitive Insights teams have done an amazing job at letting us know how frustrating these kinds of situations are. It is high on our priority of fixes."
Calling it high priority while simultaneously prioritizing everything else the studio is currently doing strikes me as a little incongruous, but game development is complex and difficult, and I wouldn't presume to question 343's allocation of resources on a project this big. That said, there are few things in gaming more frustrating than getting ganked because of a preventable connection problem—especially when that problem has been hanging around for more than half a year.
Some Halo fans clearly feel the same way, as expressed in this pointedly-entitled Reddit thread: "If fixing Desync has taken the back-burner on your priorities list 343, it’s time to rewrite that list."