What exactly does an "unstructured research problem" mean?
An unstructured problem is one that does not have a direct solution already established: that is, it's not immediately obvious how one gets from the problem statement to a working solution, or even if there is a solution.

This is the standard for most doctoral-level research problems in STEM fields: if the problem is so well-defined that the strategy for solving it is immediately obvious, it is likely unsuitable for doctoral work, and a new (usually more challenging) problem should be selected.