As far as I understand it, the "BIP-91" technique is a technique invented to abuse of the "95% consensus soft fork rule" (BIP 9), and enforce it at any level, between 50% and 95%, without having to write explicit code for that and altering BIP 9, and hence, rendering BIP 9 moot, and using the "pure hash power majority" effect that imposes a soft fork on all miners if a hash rate majority adopts it.
Reminder: without any self-restraint, any soft fork that reaches 51% of hash rate can impose itself upon everyone, without inducing a chain split. In order to render soft forks not so "dictatorship of the hash rate majority", but "full hash rate consensus", BIP 9 was introduced, that only activates proposed soft forks if they reach 95% consensus.
Of course, in reality, you better have some safety margin, because if your hash rate drops below 51%, you may see non-soft-fork blocks appear again in the chain (by the non-soft fork majority if they didn't adopt the soft fork or reverted back from it) which can be a huge mess.
BIP-91 style technique reduces BIP 9 back to potentially 51% majority over minority.
It goes as follows. Pick your "safety margin for majority" (say, 80%, or 55%, or 75%...) A.
Program the "real" soft fork under BIP 9, with 95% consensus needed to activate.
Propose a "meta" soft fork, by requiring signalling for the "meta soft fork". The meta soft fork is simply a fork that doesn't do anything particular, except requiring signalling for the real soft fork. If your meta soft fork reaches A, apply it (it is not difficult to apply it, contrary to the real soft fork which you leave to real devs: you only need to check on the signalling bit, and reject the block if it doesn't signal, that's all).
==> your A-level soft fork (not BIP9, but easily implemented) now requires that all blocks signal the real soft fork. If A > 51%, this meta soft fork is IMPOSED upon all, so the surviving chain is the one with 100% signalling for the real soft fork, which now activates because 100% > 95%.
In reality, the real soft fork has been imposed with A-level majority, not with 95% consensus, but you made the software believe that you had 95% consensus, because you applied a non-BIP9 soft fork (the meta soft fork).
In other words, this kills the idea of BIP9, while keeping it still running. Soft forks can now be imposed by any majority, even 51%, like soft forks do work.