IPA: /əˈpruːvɪŋli/
KK: /əˈpruːvɪŋli/
In a way that shows approval or agreement.
She nodded approvingly when she heard the good news.
Approvingly → It is formed from "approve" (from Old French *aprover*, meaning to test or prove) and "-ingly" (a suffix used to form adverbs indicating manner). The word "approvingly" means in a manner that shows approval or agreement.
Think of someone showing they 'approve' of something, and the '-ingly' tells us how they are doing it — in a way that expresses approval.