The fact that the side nearest the wheel isn't stiff. My existing panniers have a stiff piece on that side, and it keeps everything from flapping around.
the fold down section is quite solid.
As fossy says, the bit which is the outer cover of the stored pannier is fairly stiff so, when that's unzipped, it sits between the flexible material and the pannier guards.
Which reminds me - do get the pannier guards if you are going to use the panniers. They fit fairly quickly and easily but I would never even consider riding without them. Aside from any issues with the panniers hitting the wheels, the panniers also have a small loop of elastic which goes over the bottom of the side-pieces and holds them in place fairly solidly.
The thing is cavernous if you unzip everything. I can easily get the day's work stuff in the top section, including spare shirt and trousers, deodorant, camera and all my cycling spares. I only use the panniers if I'm carrying shoes, a laptop or the weekly shopping.