It's not so much what they do with them, although there is more ritual associated with giving and receiving them (and they look aghast at Americans who wing their own cards across a conference table).
Basically, they believe that a business card is an extension of the person and should be treated with a great deal of respect. This does result in subtle things like making sure to put their business card on a notebook or leather holder in front of you during meetings (so it doesn't directly touch the table).
