Apple Support Discussions user knicholsfl describes the issue:
Every minute or two my MBP pops up a dialogue that says,If you are faced with this situation, or if you have a MobileMe account and this message continually appears, try these steps. First, if you do not have a MobileMe account, open Keychain Access (Applications > Utilities) and click on Passwords. Look for a password entry for MobileMe and delete it. You can also find the com.apple.DotMacSync.plist file (username > Library > Preferences) and delete it."You have entered an invalid MobileMe member name or password. Verify your MobileMe member name and password in MobileMe System Preferences."The dialogue has an orange circle with the two clockwise arrows that I associate with Sync.
I don't have a MobileMe member name or password, and I haven't had one in two years. I have absolutely no idea what I did to get this to suddenly start popping up, and the start of it wasn't associated with any changes to the OS or software; there is absolutely nothing in the system prefs panel for MM, and I've tried completely disabling Sync on the computer, but it still comes up and I have to click it away. Constantly. It's slowly stripping me of my sanity.
If you have a MobileMe account, go to System Preferences > MobileMe. In the Account section, enter a gibberish username and password and attempt to log in. Ignore the error message. Now, enter your correct information and you should regain functionality of MobileMe. You should also check the Sync tab to be sure your syncing preferences are set properly.