The Loop is a lore-specific concept within Fortnite: Battle Royale. It is the idea that the Island, with everyone who is fighting within it, are trapped in a time loop.
The Loop resets every 22 minutes, as confirmed in the Batman: Zero Point comics, and it also does some things to inhabitants on the Island. Upon entering the Loop, you are completely mute, which explained the lack of voice acting in the game. The Loop also drains your memories, but the only two characters who seem to have retained them are Bunker Jonesy and Midas.
Bunker Jonesy has been part of Fortnite for so long he remembers things. He is confirmed to have been once based on the original Jonesy, having gone into a bunker in Season 9, and somehow able to age outside of the loop. It is unclear how this was possible. In Chapter 2: Season 5, you could find him at Camp Cod or Shipwreck Cove, and he'll say to the player that there is a way out of the loop.
In Update v15.40, Bunker Jonesy said that he warned us about the Zero Point. In Update v16.20, which came with the new Spire Quests, we learn that, like all the other Jonesy snapshots, he ended up losing his memory, but it was by being locked up in the Bunker for "decades, if not centuries" that he finally regained his memory and that he understood that once in the loop, we are only a snapshot of the person that we are and therefore that he is not "the real" Jonesy.
The "bunker" he got trapped in is referring to the Season 9 Cinematic Trailer, which depicted him and Peely fleeing to a bunker during the Unvaulting event. After running out of food, Bunker Jonesy was forced to blend Peely into a smoothie, and left the bunker to find a futuristic utopia. It is possible that the time gap between Season 8 and Season 9 was 10-15 years, or that Bunker Jonesy was losing his mind so much he believed that he had been in the Loop for a long time.
Due to a poor understanding of the connection between the Storm and the Loop, Midas under the IO order (Ghost / E.G.O are under the direct orders of Imagined Order as proven by the trailer of Chapter 2: Season 5 and by Bunker Jonesy during a quest of Chapter 2: Season 5) attempted to push back the storm which temporarily broke the Loop (this will allow the first meeting between The Looper and Agent Jones) and resulting in The Wall of Water.
During Season X, according to his tapes, The Scientist was forced to enter the Loop to launch the rocket.
In the season 5 trailer, Doctor Slone orders him to reenter the Loop to repair The Zero Point and prevent anyone from escaping the Loop. He eventually needed help from The Foundation, and made a deal to help The Foundation to find Geno and The Sisters. They eventually made it to the Zero Point with the Looper, which ended with The Foundation getting trapped in the Zero Point and Jones getting stuck in the Loop.
Lore Explanation and Speculation
With pieced together information from trailers and in game Easter Eggs, that the concept of Battle Royale is a loop, with every character present within it unable to remember the previous games, with their memory fading after each repeat. This memory fade has also rendered the members of the loop mute. The force that maintains the loop is speculated to be the storm, as evidenced by Midas' attempts to repeal it in The Device event. The average time of the loop is approximately 22 minutes, as evidenced by Batman in Batman/Fortnite: Zero Point Issue 1, where he has written the loop resetting every 22 minutes on his Batarang.
Battle Royale is introduced as a separate game mode to Save the World, reusing several named characters such as Ramirez and Jonesy, of which the latter is extremely important to the lore regarding the loop. Each Battle Royale match starts the same, and ends with the closing of the storm. After this, the match repeats, with the Loop remaining unaltered. Throughout the time of Battle Royale's existence, there have been many additions and changes to the island outside of the loop. It is currently unknown how this is done.
In Season 4, The Visitor, a member of the mysterious Seven makes his way into the loop via a meteor crash, and nearing the end of the season attempt to escape it using a rocket, in the Blast Off event. However, during this attempt, the rocket creates several rifts in the sky, causing a bridge between the Island and the real world, across different time periods. One of the results of this is a person from the real world, named Drift, being inducted into the loop.
After the events of The Final Showdown event, the Zero Point is left exposed, and creates another bridge between realities. This time however, it brings an alternate universe version of the Visitor, named The Scientist. The Scientist escapes from the meteor like last time, and whilst working on another rocket, starts to record tapes to try and retain his fading memory and maintain the rocket progress. These tapes detail the Loop for the first time explicitly. The Scientist succeeds, and launches a rocket alongside several unknown members of the Seven, into the zero point. As a result, the zero point expands and begins to absorb the entire island, during The End event.
After the result of the End event, a new island is created, and the loop appears to be as intact as the Pre-Season.
In this chapter, Midas first appears on the island and begins to build a device which harnesses the power of the Zero Point to push back the storm. This is unsuccessful, and instead The Wall of Water is created, flooding the entire island. The Storm being connected to the Loop was first revealed here, and this one was temporarily broken. As a result of this, of this the player is continuously transported to a mysterious office, and a familiar face interacts with the player, showing surprise that they can understand him as they came from outside the loop. John Jones is the man present, and he is the first person aside from the Scientist to be audible.
In Chapter 2: Season 4, Thor is transported to the island to warn the members of Galactus' arrival, but begins to lose his memories and voice. Due to this, he quickly brings other Marvel characters to island, and in particular, Tony Stark. Eventually, others that Thor has brought begin to lose their memories, such as Doctor Doom who quickly returns to a life of ruling, and Wolverine, who begins to stalk the woods for unsuspecting victims. However, Tony Stark somehow manages to retain his memories. Throughout the season, he works on a way to stop Galactus from absorbing the Zero Point. During the The Devourer of Worlds event, with the players help, Tony Stark manages to send Galactus far away from the Island, this however leaves the Zero Point exposed. During the event, Tony Stark mentions having 'hacked' the loop, aiding to his ability to communicate with the player, as with other members of Thor's crew.
John Jones is tasked by Doctor Slone to close the Loop, and make sure nobody has escaped, but fails to hear the warning to not alert The Seven. Despite this he goes back into the Loop to recruit various hunters from different dimensions to help him make sure nobody escapes.
In the Zero Crisis Finale, Agent Jones disregards Doctor Slone's orders to escape and to not collaborate with The Seven to reseal the now vulnerable Zero Point. With the help of The Foundation, he is able to reseal the Zero Point (if only temporarily), but as a consequence is now inside of The Loop himself.