'appetite-promoting' is a modern compound combining 'appetite' and 'promoting'. 'appetite' originates from Latin, specifically the word 'appetitus' (from 'appetere'), where 'ad-'/'ap-' indicated 'toward' and 'petere' meant 'to seek or desire'. 'promoting' comes from the verb 'promote', originating from Latin 'promovere', where 'pro-' meant 'forward' and 'movere' meant 'to move'.

'appetite' passed into English via Old French (apetit/apetite) and Middle English as 'appetite', retaining the sense of 'desire for food'. 'promote' came into English via Old French forms from Latin 'promovere' and through Middle English 'promoten'/'promote'. The compound 'appetite-promoting' formed in modern English by joining these two elements to describe something that increases appetite.

Individually, 'appetite' originally meant 'a desire or seeking' and has come to mean especially 'desire for food'; 'promote' originally meant 'to move forward or advance'. Combined in modern usage, the meaning has specialized to 'causing or increasing appetite'.