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For instance to allow meta-programming (programming code executed at compile time) in the same language as is being interpreted/compiled.

But more formally, a self-hosting compiler says stuff about the language per se, see also http://en.wikipedia.org/wiki/Bootstrapping_(compilers).

a self-hosting compiler says stuff about the language per se

That it's Turing-complete and can write to a file? I think all it really says is that somebody was hard-headed enough to do it.

Thanks for the answer and the link. I'm still trying to wrap my head around the chicken/egg problem, but that may take a little while.