The meaning reveals itself in the context.
2001's pace is purposely slow. Man emerges as a species slowly, over tens of thousands of years, man explores the stars slowly and ACTUAL space travel is very slow. The deliberately mannered tempo of the first 90% of the film reflects the unhurried pace of man's progress.
Dave's passage through the star gate is the only time 2001 really breaks loose: a passage meant to imply that the evolution of humankind was about to take a quantum leap forward, courtesy of the monolith.
The monoliths take the human race through each of its next radical jumps in evolution. The last monlith took David from human to the next stage in human evolution...the first Star Child.
The Star Child is basically Zarathustra...the Superman, the Ubermensch, the next step in human evolution. Which explains Kubrick's use of the Strauss score (Also Sprach Zarathustra) in the film.
Watched the film.