LOL! Now I know what you're talking about. You must have a Panasonic TA-824 system with BV (the built in voicemail system).
If you have a Features Manual, look at page 15. Here's a copy on my website http://public.carl.airpost.net/Pana/TA-824/400_TA_FM_07-04.pdf
Dialing 725 will get you to the BV system. Someone has filled up the message box. All those calls you get after hours will fill up the common mailbox, so someone needs to clean that box out on a hourly or daily basis. Search the file for 725 and you'll get the table that gives you instructions. The Operating Manual (OM) has specific user instructions, starting with page 36. It involves a 725 2 sequence with 3 pause 3 erasing messages. Read the section carefully, because if you mess up you will erase ALL messages.
Here's the link to the OM if you don't have it. http://public.carl.airpost.net/Pana/TA-824/200_TA_OM_07-04%5B1%5D.pdf
When you get to 5 minutes remaining in the BV system, you should have heard a funny dial tone. I'm not exactly sure if it would have been on all phones, or just the operator phone and the phone with a full mailbox. We have never installed one on a TA system in 5 years :-)