An honorific/respectful form of 'to do' (する), used to describe actions of someone superior politely; also appears as a passive form.
先生が決定をなされましたので、それに従ってください。
The teacher has made a decision, so please follow it.
会議で重要な発言がなされた。
An important remark was made at the meeting.
どうぞご自由になされてください（＝ご自由にしてください）。
Please feel free to do as you like.