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https://github.com/flame/blis/blob/master/docs/Performance.m...
It seems that the selling point is that BLIS does multi-core quite well. I am especially impressed that it does as well as the highly optimized Intel's MKL on Intel's CPUs.
I do not see the selling point of BLIS-specific APIs, though. The whole point of having an open BLAS API standard is that numerical libraries should be drop-in replaceable, so when a new library (such as BLIS here) comes along, one could just re-link the library and reap the performance gain immediately.
What is interesting is that numerical algebra work, by nature, is mostly embarrassingly parallel, so it should not be too difficult to write multi-core implementations. And yet, BLIS here performs so much better than some other industry-leading implementations on multi-core configurations. So the question is not why BLIS does so well; the question is why some other implementations do so poorly.