What is Environment.FailFast?
How is it useful?
Failfast can be used in situations where you might be endangering the user's data. Say in a database engine, when you detect a corruption of your internal data structures, the only sane course of action is to halt the process as quickly as possible, to avoid writing garbage to the database and risk corrupting it and lose the user's data. This is one possible scenario where failfast is useful.
Another use is to catch programmer errors. Say you are writing a library and some function accepts a pointer that cannot be null in any circumstance, that is, if it's null, you are clearly in presence of a programmer error. You can return an error like E_POINTER or throw some InvalidArgument exception and hope someone notices, but you'll get their attention better by failing fast :-)
Note that I'm not restricting the example to pointers, you can generalize to any parameter or condition that should never happen. Failing fast ultimately results in better quality apps, as many bugs no longer go unnoticed.
Finally, failing fast helps with capturing the state of the process as faithfully as possible (as a memory dump gets created), in particular when failing fast immediately upon detecting an unrecoverable error or a really unexpected condition.
If the process was allowed to continue, say the 'finally' clauses would run or the stack would be unwound, and things would get destroyed or disposed-of, before a memory dump is taken, then the state of the process might be altered in such as way that makes it much more difficult to diagnose the root cause of the problem.