Other forms: explanatorily
Use the adjective explanatory when you're talking about a clarification or an explanation. An abstract artwork in a gallery that consists of an old sneaker might require an explanatory note, for example.
The Latin word explanare is at the root of explanatory, and its literal meaning is "to make level or to flatten." When you give an explanatory answer or make an explanatory speech, you are laying it all out — providing all the details your listener needs to understand. Anything that makes something more clear can be described as explanatory, like a footnote in a term paper or your apologetic list of reasons for being late to your best friend's party.