The layman's explanation of how an LLM works is it tries to predict the most likely word, or sequence of words, that follow from the last. This is based all on the input training set, which is compiled into a big bucket of probabilities. All text input influences those internal probabilities which in turn generates likely output. This is also why these things are error-prone because it's really just hyper-sophisticated predictive text, and is doing its best to "play the odds."

You can also view an LLM as one fiendishly massive if/else statement that chews on text tokens. There's also some random seeding thrown in for more variation in output, but these things are 100% repeatable if you use the same seed every time; it's just compiled logic.