concept
In AI, a model is the part that does the work. It is a large set of numbers, called parameters or weights, arranged in a fixed structure and tuned during training so that a given input produces a useful output.
A language model takes text in and produces text out. An image model might turn a description into a picture, or a picture into a description. Many models handle several kinds of input at once.
A model does not look facts up the way a search engine does. It generates responses from the patterns it absorbed during training, which is why it can be fluent and still be wrong.
Example
When you type a question into a chat assistant, the model is the part that reads your words and writes the reply.