To meet or come up to a required standard (from golf where a player must do equal or better than a certain score to continue)
e.g. 1 (original meaning)
The young player did not make the cut and was unable to join the team that year.
Some say if Pluto were discovered today instead of 75 years ago, it woundn't make the cut.
(From this article about the potential 10th planet of the solar system (9 is the current recognized number), Pluto, the 9th and currently outmost planet was discredited by the newly discovered planet further away from the Sun)