I can't say for 100% its been a while since I played, but as far as I remember, they worked like this...
You placed a passport box along a path, it was a little brown box like a trash bin, and sometimes guests would walk up to it. Then if you clicked on their profile info, it would let you know where they have been (and I think it showed a stamp/icon). You could name the passport box and designate it to a certain area or theme. I could be wrong because it never seemed to work properly for me, but you could offer free items in exchange for the stamp/tokens, at certain shops for like souvenirs. So, you could have a special hat that is only sold to guests with a certain # of tokens.
At least, I think that's how it worked.