Sphoof is a DIY framework, favouring freedom over convention or configuration, by assuming little about how you want to write your applications. It gets out of your way as much as possible, while trying to give you a solid, well thought-out and very extensible base to work on. There's a number of places where you can stick your own code and use that instead of our default code. It's based on the MVC design principle, although it leaves the most important choices of implementation in your own hands.
It's trying to be as restful as we can consider practical. It has a default implementation for routing - of sorts - and it closely maps to the HTTP protocol.
It's not a full-stack framework: there are things it simply can't do, because there are tons of libraries that do the same in a way we're comfortable with. We're just trying to improve what's worth improving, not trying to reinvent the wheel.
Good question. With so many OO frameworks out there right now, it's hard to imagine there is even the smallest of markets for a new one. Still, we've found other frameworks to be too dictating, insufficient, or promoting to write code you don't like to see. It has started as a learning-experience, but thanks to the entusiasm of our contributors, it has grown into a framework on it's own.