My Mac OS X time changed automatically to Jan 1, 2001?

When you connect to the internet if set up in the Date/Time Preference Pane the computer will retrieve the time from a time server (in this case, most likely time.apple.com) and set it to the proper time. If the time is being reset to January 1st, 2001 you most likely have a dead PRAM/Clock/CMOS battery or something odd happening with your PRAM.

You can try resetting your PRAM but restarting and holding the Command-Option-P-R keys down until you hear the computer start up (the "bong" sound). If that fails to work you'll need to replace the battery which is easiest by taking it to a Apple Authorized Service Centre. These batteries normally last 7-10 years.

Most probably the cell that powers your MacBook's internal clock may have drained. When you connected to the internet, the operating system most probably updated the time using NTP.