From what I have seen and read on blogs, PyPy is a very ambitious project. What are some advantages it will bring to the table over its siblings (CPython, Jython, and IronPython)? Is it speed, cross-platform compatibility (including mobile platforms), the ability to use c-extensions without the GIL, or is this more of a technical exercise on what can be done?
cross-platform compatibility

Yes
What does PyPy have to offer over CPython, Jython, and IronPython?