It's basically what it sounds like: slowing down and being mindful of what is or isn't working for your family. It's not so much saying you can't enroll your kids in any activities or classes, but just to be mindful as to whether or not it's actually nurturing the family connections that are important to you.
If you're curious, there's a lot more information in this article about the movement started in Austin by the co-founders Contey and Noll. You can also check out their website, Slow Family Living.com.
(Image: Slow Family Living.com)