For example, at a certain size, GPT models start to "learn" how to do basic arithmetic (addition), even for numbers with multiple digits they've never encountered before.
It might look like a small thing, what with computers being quite able to do arithmetic at the base level. But this is a language model, so its a bit different. It learns how to add numbers without "carrying the 1" first, then at a certain larger size also learns to carry the 1, then when even larger it learns to do that across multiple digits... So its not just blindly guessing, its learning the rules of the game (and in some cases some quite complex rules) by building a model of the world made of words.
And the model of digits and addition is just one small bit most likely, as the training space doesn't contain much of that - writing about adding numbers is pretty boring after all. The full model must encode rules and knowledge about a variety of complex things to be able to make reliable predictions. It probably also contains true generalizations that humanity hasn't thought of before, as well as specializations of those generalizations that could be immensely useful.