it provides a way to an increase call volume without adding more lines.
many voice mail systems can take messages form several callers simultaneously without giving a busy signal, even if you have only one line.
you can leave detailed messages in different mailboxes for specific groups of callers. this cuts down on callbacks.
many voice mail services also offer sophisticated features like selective playback and retrieval which allows users to skip through messages save and forward them things you can't do with an answering machine