There's a few things that make that site so very very cool in my mind.
First, it's just fun to see my pups family tree. I use it to show off to friends and family (Ferrari Dog! :smiling_face_with_open_mouth_closed_eyes: ). I use it to contemplate the conversations and thought that might have gone into a breeding say... 4, 5, 6 generations back... that may have created the strongest attributes I might be seeing today. The pictures make that really fun to noodle.
Second is being able to see which breeders have relationships e.g. my breeder, Astarte is closely aligned with Kazor and Taji. There're more, but you get the idea. Why would that be important? Well, I would guess that a person trying to find a puppy might be able to use it as a tool to identify breeders who may not be listed on sites like AKC or BCOA. Sure, it would take a little digging, then some google searches, but to me... half the fun is the hunt. Ask any squirrel hunting Basenji. I can't believe more people aren't using the database for this purpose.
Third, to check health as has been mentioned e.g. Fanconi, PRA, hip dysplasia
There is so much involved in being an ethical and successful breeder. The database gives an indication of both. A person can spot a championship line and see that it's been happening for generations spanning decades. I can go back 5 generations, BUT... if I go to Logan's Great great great grandmother and search her... now I get to see another 5 generations back. Take some notes and do some google searches. It's like a treasure hunt clues. Having a basenji has become a hobby, so I love this stuff. Thanks @Zande