IBM, which was contracted by National Center for Supercomputing Applications at the University of Illinois in Urbana-Champaign, is said to have abandoned the project as the "technology […] was more complex and required significantly increased financial and technical support by IBM beyond its original expectations."
A press release indicated that the two parties could not find a mutual plan that would accommodate the changed environment. As a result, the NCSA is getting its money back. IBM will also get back all equipment that had been already delivered.
Blue Waters was originally planned to become NCSA's new flagship supercomputer with a peak performance of 10 PFlops that should have been delivered by at least 300,000 IBM Power7 cores. The original core architecture promised a quad-CPU module, which holds four 8-core Power7 processors. Each processor was promised to deliver a peak performance of 256 GFlops and each module about 1 TFlops. Other specs included more than 1 PB of memory, more than 25 PB of storage, 500 PB of archival storage and more than 100 Gbps of bandwidth. The NCSA said that it has not abandoned the project, but is looking for other ways to realize its next supercomputer.
I would suspect simulations and problem solving algorithms that would take days, if not weeks on ordinary computers. One of my electronic engineering teachers told us he did his thesis would've taken weeks to do in an ordinary computer, and he did it in 2 hours on his university's supercomputer.
And neverdyne is correct, things like Meteorological models would be calculated on this. A lot of math problems take forever to do out, even with a modern desktop computer, so they build supercomputers to grind the numbers.