There is no real "Intelligence" behind these models. In reality, this learning happens at a deeper level and consists of algorithms that create relationships between a given subject/term and other similar ones (semantics), through the use of vectors. Because the models are trained with a lot of data, the AI ends up having a very broad context window about any subject it was trained on.
Disinformation generated by AIs
It is important to note that the quality and types of responses from a model will depend on the quality of the material provided during training. For this reason, this is one of the most discussed topics today, see — The impact of AI on disinformation and democracy
The Large behind the acronym refers to the complexity and processing power required to run these models. For this reason, most LLMs currently available are offered through APIs or external applications.
There is also a recent discussion about Small Language Models, with lower processing power, but which can run in "less robust" environments.