A model whose trained numbers (weights) are published so anyone can download them.
The heart of an AI model is a huge set of numbers fixed during training, called weights. An open-weight model publishes those weights as files, so anyone can download the model, run it on their own machine and adjust it. A closed model stays on the company's servers; you can only talk to it through an app.
How "open" a model is varies. Many release the weights but not the training data or the full recipe, and some attach rules about how you may use them. That's why people argue about whether these models should be called "open source".
Think of it like this
Imagine one restaurant that only delivers meals, and another that hands you a whole jar of its secret sauce. With the jar, you can take it home and cook with it your own way. Open weights are the jar, but you often don't get the recipe that says what went into it.
For example
Download the weight files and, if your laptop is powerful enough, you can run the model with no internet at all.
Records about this
Source-checked moments from AI history.
Established the grounds for ruling that most of Llama, Gemma and Qwen are not open source
Popularized open weights, and the starting point of the debate over whether it is open source
The first large attempt to distribute frontier-class weights after vetting