忙不迭 is an adverb meaning 'in a hurry' or 'hurriedly', but it carries a specific nuance: it describes doing something hastily because you feel compelled or pressured — often out of politeness, eagerness, or to avoid being rude. It's a set phrase (three syllables) used before the verb it modifies, typically in narrative or descriptive contexts. You won't use it in casual everyday speech like 赶紧 or 急忙; it's more literary and vivid.