The system that allows you to leave your friend a message when they don't answer their phone is called voicemail. The message you leave can be called a voicemail as well.
Leave your mom a recorded message when she doesn't pick up your call — that's a voicemail. The word was coined by a company that first developed a voicemail system available across the U.S. — earlier systems called them "voice messages." Originally, Voicemail was capitalized and trademarked, but it quickly became the general term for electronic telephone audio messages.