The two characters combine literally to mean “at that day.” The character 当 (dāng) pinpoints the action to the specific 日 (rì) being discussed, creating the precise meaning of “on that very day.”
The use of 当日 reflects the value of precision and formality in certain domains of Chinese communication. While daily conversation thrives on context and informality, areas like law, history, business, and journalism demand clarity and the removal of ambiguity.
当日 is frequently encountered in written and formal contexts. It's less common in casual chats.