remaining life; time left to live
Often used in serious contexts such as terminal illness, life expectancy, or the limited time one has left. Can be used both literally and figuratively.
The doctor told me I had six months to live.
He decided to spend his remaining days with his family.
The doctor told him he had three months left to live.
He was given a terminal prognosis.
I want to do the things I want to do before my remaining life runs out.
The new treatment was able to extend his remaining life.
命 is the broad, everyday word for 'life' itself, while 余命 narrows the focus to the specific amount of time left to live.
Compound of 余 (yo, 'remaining') and 命 (mei, 'life'). The reading よめい is a standard on'yomi compound.