Open-weight models
A model is open-weight when its trained parameters (its "weights") are released publicly. Anyone can download the model, run it on their own computer, look at how it works, fine-tune it for a new task, and keep their own copy indefinitely. The model is not necessarily open-source in the full sense since its training data and recipe may not be shared.
This is the opposite of a closed-weight model, where the only way to use it is to send your input to a company's servers through an API.
The distinction matters for Data sovereignty. An open-weight model can run entirely on local hardware, so no language data ever has to leave the community, and the system keeps working even if a vendor changes its terms, raises prices, or shuts down. Open-weight models are often small enough to run on ordinary hardware.