to use up; to exhaust (resources, money, supplies)
彼は貯金を尽くして店を開いた。
He used up his savings to open a store.
燃料を尽くして、車が途中で止まってしまった。
They ran out of fuel and the car stopped on the way.
材料を尽くして料理を作ったので、もう残っていない。
I used up all the ingredients to cook, so there's nothing left.
to devote oneself to; to do one's utmost for someone or something; to serve
彼女は患者に尽くす優しい看護師だ。
She is a kind nurse who devotes herself to her patients.
両親は子供のために一生尽くした。
The parents devoted their lives to their children.
会社のために尽くしたいと考えている若手社員が多い。
Many young employees want to devote themselves to the company.
suffix attached to the -masu stem meaning 'to do something completely / to the utmost' (e.g., 食べ尽くす = eat up completely)
町中のパンを食べ尽くしたわけではないが、かなり回った。
I haven't eaten all the bread in town, but I visited quite a few places.
アイデアを出し尽くしても、まだ新しい方法が必要だ。
Even after exhausting all ideas, we still need a new approach.
本を読み尽くして、棚が空になった。
I read all the books and the shelf became empty.