It predicts the next word.
A large language model plays one game, over and over: guess the next word. Your phone's autocomplete plays a tiny version of it. An LLM plays it with a vastly bigger sense of how language usually goes.
For every position, the model outputs a probability distribution over its whole vocabulary. Everything it produces, from code to contract summaries, is a sequence of draws from those distributions. Temperature reshapes them: low is predictable, high is varied.
Drag temperature all the way left and sample ten times. Then all the way right. Which setting would you want writing a birthday poem? Which doing your maths homework?
Open "The capital of Australia is". The wrong answer has real probability because it's common in text. That's the root of confident errors, and why verification belongs in your workflow.