再 began, scholars believe, as a fish trap raised again for another catch — the essence of 'one more time' drawn as equipment reuse. Whatever the picture, it has meant 'again' for three millennia.
再 is the last word most learners say each day: 再见 ('see you again' — goodbye). It sequences actions too: 先吃饭，再学习 (first eat, THEN study). 再来一个! ('another one!') is what you shout at performers, and 再三 ('again-thrice') means repeatedly. A character entirely about not stopping.
The trap goes down AGAIN for one more fish — AGAIN.
再见 'again-see' is exactly the same construction as French au revoir and German auf Wiedersehen — great minds part alike.