heterodox - What does it mean for atheists to raise their children 'Jewish'?

I was reading the book Battle Hymn of the Tiger Mom by Amy Chua. In this book she mention that her Jewish husband is not religious in the slightest but still when they got married insisted that the children where raised 'Jewish'. I'm curious what exactly to be raised Jewish means in a general sense (as opposed to what it means to Ms. Chua specifically), especially considering that it is important for non-religious Jews as well.