> is it understanding the underpinnings of the biology behind a particular pathway you're studying
Yes, this is it. You are right that the really general basic concepts (what is DNA? how does transcription work?) are not all that hard to learn. And it is certainly part of the core job skills to know, e.g., how to process sequencing data and how to use statistics. But in the real world, bioinformaticians work in collaboration with wet-lab biologists.
So, a typical project for me might look like this: collaborator comes in and tells me that his lab studies a particular protein X that operates at the presynaptic terminal in neurons. And they are collecting data about how some perturbation to X affects other cellular systems. The data will often be some combination of sequencing/array data and more specific wet-lab experiments (western blots, electrophysiology, etc).
So, in that case, to really do my job well, I have to go back and read in depth about the presynaptic interface, the major proteins and the mechanisms that work there. I may already know the generalities, but to really be able to interpret the data correctly, I need to know the details.
Now, imagine doing this process 10-20X a year for different collaborations and totally different biological systems. It's very hard to keep up. Now, it is certainly possible to be the kind of bioinformatician who is "give me your sequencing data and I'll give you the DE genes back", treating everything as a purely technical problem. But these kinds of bioinformaticians are not as much sought after because the wet-lab biologist doesn't want Excel spreadsheets full of lists, they really want to know "what do my results mean?". And to answer that really requires both the bioinformatician and the wet-lab biologist to understand what the other is doing at a more than superficial level.
In short, the hard part isn't learning the things that are used in every project, the hard part is learning the domain-specific information that is relevant to each individual project.