Perhaps I used the term too loosely, as pointed out it’s a broad term that can vary depending on the specific topic. In the context of my post you can take it to mean values that are free to change independently. Temperature or cloud formation, for example, would be a fully dependant variables, as you have no freedom to set them. Instead they are completely a function of the physics in the model itself. In a statistical model on the other hand, virtually everything is potentially an independent variable.
For the study of CO2 the only variable that would change would be CO2 concentrations. In practice, there are indeed parameters in a climate model that can be set, but these represent observable physical behavior so their value cannot be arbitrarily entered by the modelers, though different modelers may rely on different sources for it’s value and therefore get slightly different results, which is one of the reasons the IPCC uses ensembles of different model runs.
Realclimate has a good article on how parameters are used and handled in climate models.
http://www.realclimate.org/index.php/archives/2009/01/faq-on-climate-models-part-ii/