• 退職たいしょく — retirement
• 退学たいがく — dropping out (of school)
• 退院たいいん — discharge from hospital
• 引退いんたい — retirement (from work/sports)
• 後退こうたい — retreat; falling back

退 combines the idea of legs and the 辶 (movement) radical, expressing the action of stepping back. It is used widely in contexts of resignation, withdrawal, and retreat — from politics to personal life events.

彼かれは 会社かいしゃを 退職たいしょくしました。
He retired from the company.

病気びょうきが 治なおって 退院たいいんしました。
I recovered from illness and was discharged from the hospital.