no fear, its the built in "windows messenger" service, which was implemented mainly for server applications to send notifications to other workstations to inform them of reboots and such like.
To disable it, click start->run, type services.msc.
Scroll down the list and find "Messenger".
Right click, choose properties, click the stop button, and then in the list choose disabled. and click ok
That will stop the messages coming ...
To get those messages in the first place, it sounds like your pc is connect directly to the internet, i.e a modem on your pc rather than a router.... if this is the case, you really need setup a firewall!
If you are using windows xp, you can enabled the built in firewall:
start->run, type firewall.cpl
or goto the control panel and choose "windows firewall"
you can enable it there.
If you don't have windows xp, I suggest installing Zone Alarm
Hope this helps!