When there is a new message in your voice mailbox, your dial tone will change from a continuous tone to an intermittent one in the first few seconds. Your landline phone will "notice" this and will turn on the "new message indicator", which is usually a red LED flashing. Once you listen to your message, the LED will stop flashing.

A well known bug with many phones is that they are quick to get the LED flashing, but they don't always notice that the dial tone has returned to normal. Most phones include a way to cancel the flashing when it won't turn off by itself. Please consult your phone manual for ways to achieve this.