A "high-assurance application" is one that the NSA cares about, so will actually spend their money to fund a research project. Otherwise, it is awfully hard to get funding for PL research.

Edit: please read the website, this really is funded by the NSA.

I'm pretty sure that's just supposed to mean "applications that you really want to not have bugs in". Like code that will be dealing with large amounts of money, say. The web page is pretty light on details; I get the impression that Wyrven is something they're using more as a research platform at this point than as something for developers to actually use.

I took this to mean code correctness and thus a measure of stability and security as added benefits. Generally assurance implies some level of confidence that the application will behave predictably even in the face of unpredictable inputs and will revert to sane defaults whenever possible.

I believe it is known as a buzzword