This solution was posted at Macintouch a while back:
A couple of years ago, Apple released a software update for 10.6 (Snow Leopard), 10.7 (Lion) and 10.8 (Mountain Lion) systems called "Mac App Store Update 1.0". This had a somewhat vague description about improving the App Store.
One of its features is that it installs a "noticeboard" mechanism on 10.6 and 10.7 systems, which periodically checks with Apple to see if there are any messages to display. If there are any messages, they appear as an alert in the middle of the screen. 10.8 had a similar mechanism added, but it was implemented differently and using Notification Center to display the message. The equivalent of the 10.8 implementation is built in to 10.9 and later systems.
Apple was originally using this to push notices about upgrading to the latest OS X (which was Mavericks at that point), at a rate which felt like about once a month. I haven't been paying close attention to the pattern, but I have some Macs still running older systems, and my gut feeling is that Apple have dialled back the rate of notices appearing since the mechanism was introduced.
The mechanism has nothing to do with Software Update or App Store checks for updates, and there is no user setting to disable it.
On 10.6 and 10.7 systems, this should disable it for the current user:
launchctl unload -w /System/Library/LaunchAgents/com.apple.noticeboard.plist
You enter that in Terminal.