Running that access point at home, or somewhere else, allows you to StreetPass with people who pass Nintendo Zones all over the place. If you live in a very rural area (like I do) or you don't go to many places where you can get other local StreetPass hits, it makes the StreetPass games actually playable.
Impressive detail, but (as with a great many tech how-to guides) I struggled to find an explanation of why you might want to do this.
Because it's a very easy way to find local players who have passed by the router in the past 12 hours, and automatically exchange friend codes.