Busy is a VERB. (Action) = To be very involved in an activity or many activities.
Examples : I am busy. You are busy. He was busy. She will be busy... etc.
Busily is an ADVERB (Describing word) telling HOW someone was doing / in what way.
Examples: I seemsed hurried, busily cleaning my desk. (HOW did I clean it?)
Yep, you got it now... :)