I believe that a layman's explanation is that BIP91 facilitates (or forces) the locking in and activation of segwit, which locking in adn activation of segwit process will take place in August.
BIP91 also causes some attention to a possible 2mb blocksize limit increase through a hardfork - however, the language of BIP91 does not seem to mandate those further steps regarding 2mb increase or the hardfork.
So the more important thing about BIP91 seems to be providing a vehicle or a channel to activate segwit - which also nullifies the activation of BIP148 (User Activated Soft Fork) that would have gone into effect on 8/1.
Can anyone say more than that would be more concrete than speculation?
Segwit2x does not have a valid BIP. Miners were meant to signal their intent to fork with segwit2x by adding NYA to their coinbase. BIP91 was proposed by James Hilliard as a way of making segwit2x compatible with BIP141 (the original core segwit activation). Thus it does not have anything to do with the 2x hard fork component in the future. The only thing that says miners are for both is the presence of NYA in their coinbase, which doesn't even activate anything in particular, it's just a comment, along with the continued signalling on bit 4. You can see why the hard fork is precarious in light of this.