It's just another type of non-volatile storage.
Memristors, the way they are hyped, promise to be orders of magnitude smaller, faster, cheaper AND less energy consuming than all of the other memories that exist. All at the same time. If time proves this all to be true, it can bring really groundbreaking changes to computing. And we all will be able to watch more funny cat videos, at a greater resolution.
Taking advantage of such systems will not be business as usual, it'll look even more foreign to us than CUDA does to a Javascript developer.
Sure, you can use an interface and use them just like a regular storage device, but until and unless you can get the cost per bit below flash it's not interesting at all.
If that was all memristors could do, it's not even clear that they would be in active development - this is a moon shot by HP (no pun intended).