one's remaining years; the rest of one's life
Refers to the period of life after a major turning point, such as retirement, recovery from illness, or a life-changing event. Often carries a reflective or serene tone.
After retirement, he spent the rest of his life quietly in the countryside.
After a serious illness, she decided to devote the rest of her life to community service.
老後 emphasizes the retirement lifestyle and its financial/practical side, while 余生 emphasizes the remaining time one has left to live, often with a reflective tone.
Composed of 余 (surplus, remaining) and 生 (life). The exact historical derivation is uncertain, but the compound has been used in literary Chinese and Japanese to mean 'remaining life'.