When you do something reprovingly, you do it in a scolding sort of way. Ask your studious friend if she wants to stay up late watching movies and she'll reprovingly say, "We have a math test tomorrow."
If your grandma glances reprovingly at you during dinner, you might want to check yourself: are your elbows on the table? Are you chewing with your mouth open? This adverb is perfect for action and speech that criticizes, rebukes, or disapproves. Bring your adorable puppy into a busy restaurant and some patrons will most likely exclaim over her — but others will probably frown at you reprovingly.