Think of passbook as an aggregator. In it's present form, it's similar to those keyring apps that hold all your loyalty cards, but on steroids. At present, is supports loyalty cards, tickets, boarding passes, and gift cards/payment cards from some vendors.
The advantage of using passbook over those other apps is that it's all in one location. Instead of having to open your United Airlines app, the boarding pass is stored in passbook, same for your Walgreens loyalty card, same for your Starbucks card, same for your baseball game ticket. In addition, it also offers geofencing, so that it pops up on the lockscreen when you're at a specific location. For example, if you're at Starbucks, the Starbucks card will automatically pop up on the screen. If you're at the airport, your boarding pass will pop up. It doesn't always work right, as people have said, but I'm sure it will get better. Eventually, after some major changes to worldwide payments systems infrastructure, passbook could conceivably be used as a wallet replacement. Electronic wallet is still in it's infancy, it'll take a bit of time before standards are realized and a significant number of vendors have the necessary equipment to accept payments via cellphone. Hopefully sooner rather than later.