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.
Being "Raised Jewish" in this context means that, to the degree that there is any religious experience in the home, it is of Jewish origin. So if they go to a house of worship, it will be a synagogue. If they do something of a religious commemoration in the month of December, it will be Chanuka, and most significantly if the child asks what religion they are, they will be told "Jewish".
The specific practices above are only common examples. Another very popular one in America is attending a Seder on Passover.
Jews, even if they don't particularly practice their Judaism, often have a strong identity as "Jewish" and can want to pass that identity on to their children. (See here for such an example). So exactly what form that takes will depend on what practices they were themselves particularly impressed with as children, but the general sentiment is this: They aren't particularly concerned with their children practicing the Jewish religion but they do want them to identify as Jews.