Honorific term used to refer to another person's nephew, showing respect toward that person or their family. Not used for one's own nephew.
社長の甥御さんが来月結婚されるそうです。
I heard that the company president's nephew is getting married next month.
お宅の甥御さんはどちらの大学に通っていらっしゃいます
Which university does your nephew attend?
甥 is the plain word you use for your own nephew, while 甥御 is a polite term used to refer respectfully to someone else's nephew.
Standard kanji spelling for this honorific term.
Mixed kanji-kana spelling; less common but still encountered.
Compound of 甥 (おい, 'nephew') and the honorific suffix 御 (ご).