All this fancy phrase means is that after we solved the model, we change the values of some exogenous variables and see their effects on the solution values of the endogenous variables. In economics, we generally write models to analyze the equilibrium states of the economy or different markets. As you know equilibrium means the state of rest. It is a state in which things are static: they are not changing. There are no incentives for them to change. They will change, however, if one or more of the exogenous variables change. So a comparative static experiment means comparing two static (read equilibrium) situations to each other as a result of changing some of the exogenous variables.
For example, we try to answer the question: what will happen to national consumption if national income increases by 10%. The answer to such comparative static questions is also called the prediction of the model. For example, our model may predict that a 10% increase in national income would result in an 8% increase in national consumption.