A very large pattern-matcher trained on enormous amounts of text. What people mean when they say 'AI' these days.
An LLM is a computer program that learned to predict the next word by reading most of the writing on the internet. That's it. That's the magic trick. If you give it a half-finished sentence, it can guess what comes next so well that the answer feels intelligent. Because it learned from so much text, it has absorbed facts, grammar, code, reasoning patterns, and writing styles. ChatGPT, Claude, and Gemini are all LLMs.
Understanding that an LLM is predicting text, not looking things up, explains almost every strange thing it does: why it can hallucinate, why prompting works, why it's amazing at some tasks and terrible at others. It is a very smart writer. It is not a database.