Seems they're claiming they can find a predictable output from the hash function.
For those unaware, a cryptographic hash function should ideally take an input of arbitrary size and produce a fixed size output with the following characteristics:
- even distribution across key space - non-trivial predictability of input from output - completely uncorrelated output from input
It's the last feature that bitcoin relies on, which is that we need to take a given input (the block details) and come up with a random bit of information (nonce) to add to it such that the resulting hash output has certain arbitrary characteristics (i.e. begins with n number of 0s).
If they've found a way to make a hashes output more predictable such that you could determine an input that is likely to produce a given output, they could take a block, a randomly selected output with the proper characteristics, and find the appropriate nonce so as to achieve that hash output.