There are VERY FEW fully open LLMs. Most are the equivalent of source-available in licensing and at best, they're only partially open source because they provide you with the pretrained model.
To be fully open source they need to publish both the model and the training data. The importance is being "fully reproducible" in order to make the model trustworthy.
In that vein there's at least one project that's turning out great so far: