Refers emphatically to that man himself; indicates that he personally or directly (and not someone else) is involved.
会議には彼自身が出席した。
He himself attended the meeting.
その決定は彼自身の意志だ。
That decision is his own will.
彼自身の言葉で説明してもらいたい。
I want him to explain it in his own words.
問題を解決するのは彼自身の責任だ。
It's his own responsibility to solve the problem.