It's a bit complex, and you can find a better answer elsewhere, but a model is a set of "weights" and "bias" that make up the pathways of the neurons in a neural network.

A model can include other features but at its core it gives users the ability to run an "ai" like gpt, though models aren't limited to only natural language processing.

Yes, you can download the models and run them on your computer, generally there will be instructions in each repository, but in general it involves downloading the model which can be very large and running it using an existing ml framework like pytorch.

It's not a place for the layman right now, but with a few hours of research you could make it happen.

I personally run several models that I got through huggingface on my computer, llama2 which is similar to gpt3 is the one I use the most.

The model is the brain, you use something like Kobold.cpp to load the model. You'll have to work with the settings and try different models to get the right load on your GPU.