Any way you add them up, horizontally, vertically, or diagonally, you get the same sum. Of course we had to get on the internet to find out more. We found alot!
This one also has some other interesting properties:
Try adding up corners or the 4 center squares. Pretty neat, huh? This one came from a website here: http://mathforum.org/alejandre/magic.square/adler/adler.whatsquare.html
Here is a nice explanation of them, along with some interesting historical magic squares and variations, including one by Ben Franklin!: http://mathforum.org/alejandre/magic.square.html
This site also has lots of links to other magic square sites.
Here is an interactive magic square puzzle: http://www.dubster.com/math/
Here you can print up some magic square worksheets to fill in missing numbers: http://www.blackdog.net/games/math/worksheets/magic/
I think this is enough to keep us busy for awhile!