[yaakov34]

I don't know who applied it to LLMs, but it is/was the standard term used for an image processing model producing a detailed signal not justified by its inputs. For example, "face hallucination" means that the model produces a detailed-looking face when given very noisy data, but of course the face will not actually be the original face. In fact, the original image may have had no face at all. Hallucination can be either desired (as a kind of generative technique) or very harmful - imagine using image enhancement to identify a criminal in a noisy image, and getting a detailed face looking like someone in your training set - but not the right person's.

Any image enhancement technique, deep learning-based or not, can result in hallucination - you're producing information which was not in your input, which you're able to do because you have priors. But this can always result in incorrect information.