I just came across the concept on The Cherry Blossom Girl blog (pics are all hers - she visited one!). Cat Cafés have recently become all the rage in Japan. Most Japanese apartments don't allow pets, unless it's a large family apartment, so this is why a Cat Café is a popular concept there. As the name suggests, it's a coffee shop filled with cats where you pay by the hour to get to spend time with the feline furries! Many people use it for stress relief and companionship.
If you're interested, read this article on the phenomenon, it's really quite interesting. They visit one, explain all about it and how it applies to the Japanese lifestyle and social culture, and they even interview a few cat café visitors.
Here's a random video that shows a bit about it...
Images by The Cherry Blossom Girl.