I have to ask this, because: The only thing I recognize is, that if the assertion fails, the app crashes. Is that the reason why to use NSAssert? Or what else is the benefit
I can't really speak to NSAssert, but I imagine that it works similarly to C's assert().
assert() is used to enforce a semantic contract in your code. What does that mean, you ask?
Well, it's like you said: if you have a function that should never receive a -1, you can have assert() enforce that:
void gimme_positive_ints(int i) { assert(i > 0); }
And now you'll see something like this in the error log (or STDERR):
Assertion i > 0 failed: file example.c, line 2
So not only does it safe-guard against potentially bad inputs but it logs them in a useful, standard way.
Oh, and at least in C assert() was a macro, so you could redefine assert() as a no-op in your release code. I don't know if that's the case with NSAssert (or even assert() any more), but it was pretty useful to compile out those checks.