To do something with one's utmost effort; to work very hard or earnestly.
試験に合格するために一生懸命勉強した。
I studied very hard to pass the exam.
彼は仕事に一生懸命取り組んでいる。
He is working on his job with all his effort.
子どもたちは一生懸命に走ってゴールを目指した。
The children ran with all their might toward the goal.