A model whose parameters you can download and run.
Open-weights models publish the trained parameters, so anyone can run them on their own hardware, inspect them, or fine-tune them without asking permission.
This is not the same as open source: the training data and code are usually withheld, and licences often restrict commercial use or scale.
The practical appeal is control — data never leaves your infrastructure, the model cannot be deprecated underneath you, and cost becomes hardware rather than per token.