Duty, responsibility, or charge; a task or role assigned to someone. Often used in compounds and is somewhat formal.
彼は新しいプロジェクトの任を受けた。
He accepted the responsibility for the new project.
任務（にんむ）という言葉はこの『任』が語根になっている。
The word 'ninmu' (mission) uses this character '任' as its root.
重い任を背負うことになったが、彼は覚悟を固めた。
He ended up bearing a heavy responsibility, but he steeled himself.