I always thought “the one” was a reference to his UID. I figured the 1990s era computers in the Matrix still used 32 bit values and rolled over on every 4 billionth person. The person who snagged UID 1 (ok, technically it should be 0, but whatever) got superuser privileges in the Matrix.
The later movies kind of crapped on this theory, but they didn’t replace it with anything that made sense, so I kept it alive in my head. This also goes with my theory that the Matrix was designed by humans to keep the population alive until the nuclear winter passed after the war that nobody talks about anymore. The whole human battery thing was just a total misunderstanding by the rebels (or maybe propaganda?) that didn’t make sense anyway.