Here's the premise: Sign up, put some cash in your Twitpay account through another payment service like PayPal, and then send out a "tweet" to another Twitpay member, structured like "@josh twitpay $10 for beers." Twitpay takes a five-cent commission. Its founders are hoping that, eventually, it can be used for charity and disaster relief payments.
It's a nifty idea, though not for everyone. You don't get cash out of it, for example--Twitpay reimburses you in the form of Amazon gift rewards instead. Also, I'm not sure I always want to make it public that I'm letting @josh pay for my beer (don't want my Twitter followers thinking I'm a lush and a mooch), and Twitpay doesn't work with direct messages or friends-only Twitter accounts. You can, however, go to the Twitpay homepage and use that in lieu of a formal tweet.
According to Twitpay's FAQ page, the app was created "because Silicon Alley Insider said it was a billion dollar business (and) a billion dollar business sounded good to us." Indeed, micropayments are a hot topic in the social media world as an alternative to advertising-based models--Facebook has had a payment system in the works for what seems like a zillion years.
And, perhaps, it's something on which Twitter itself, still lacking a concrete business model, could capitalize. The company already bought Summize to power Twitter Search; having a payment system on board could sure help with those marketing promotions that are all the rage these days.