The model produces the most likely continuation; it does not check truth values. If it has no solid basis, it still comes out with a grammatically flawless, convincing sentence — because that is what it was built to do. This is the other side of the very capability that makes it useful at all.
It is measurable, and it is not solved. On the easiest task — summarising a single document handed to the model — the best models have come down to a 2% error rate — but that number only means something read together with the answer rate: one model leaves every fifth question unanswered. On harder, lifelike tasks they are far worse: in a study that had professional journalists rate more than 3,000 answers across 18 countries and 14 languages, 45% of the answers contained at least one significant error.
The most common misconception is that it only covers invented facts. It does not: it is still a hallucination when the model cites a real source that does not say what it claims. That is the more dangerous case, because the reference is clickable, and that alone makes it look credible.
The mechanism and five practical ways of reducing it are covered in why AI makes things up, a separate article. The directly related terms: RAG, guardrail and temperature.