Simple and common. Technically this is a message key, not a voicemail key. Someone else turned on this extension's message key.
What is the difference? Well if it was a voicemail key then it would always call the voicemail system. You will notice that this button does nothing while when it is not blinking.
Traditionally a lot of PBX systems have a message key. Another extension can turn on this key to request that the person calls them back. When that person calls back the 1st party, and the original person picks up the phone, then message LED should clear.

The easiest way to clear this is to dial the code #409 on the phone that has the blinking MSG key.