At the end of The Matrix, Neo embraces his role as the One by taking flight for the first time. Throughout the movie, whether or not Neo was “The One” was up in the air, especially from his visits with The Oracle.
In The Matrix, The One is a very special person who possesses great power inside the Matrix itself, which translates to the real world in the sequels. Morpheus was convinced that Neo is The One, so he brings everyone on the Nebuchadnezzar along in trying to find Neo before the Agents can.
At the end of The Matrix, Neo is shot and killed in the Matrix by Agent Smith, but that doesn’t stick. Back in the real world, Trinity tells Neo that the Oracle told her she’d fall in love with The One. As she kisses Neo, he comes back to life. Within the Matrix, Neo can suddenly feel and control the Matrix, and he ends up destroying Agent Smith without difficulty. Neo later sends a message that threatens the machines, then flies away.
Despite his initial doubts, Neo really was The One. At the end of The Matrix, he’s embraced that destiny and has incredible power. While the Agents were powerful, they were still restricted by parameters set for them in the Matrix. Neo, on the other hand, was able to manipulate just about any part of the system however he wanted. Flying off is one of the ways he shows just how much power he has; not only did he defeat all the agents, but now even gravity is no longer a limit for him.
Neo's ability to take flight also sets up much bigger things to come. While The Matrix sequels took a while and ultimately disappointed fans, but the original film's ending clearly sets up that more could happen in the world, expanding it and the potential of what The One can actually do. Even if no sequels ended up being made, Neo was clearly set up to be able to do much more in the future. Being The One isn’t just about the power Neo has, but is about saving humanity from the machines. The Matrix's ending proves Neo’s story is about to get bigger, and flying at the end makes it something else. Instead of the more grounded cyberpunk story it had been originally, Neo steps out of a phone booth and flies off like Superman. His newfound powers and mission basically make him a superhero, so what better way to show that off than by giving him the ability of flight?
Having embraced his power as The One, Neo shows those powers by flying off at the end of The Matrix. His mission is much bigger now, so he has the increased power to match with it that aids the franchise's future installments, which go into much crazier places.
