The "Model" price is a math model of the probability of a default by the time the CDS expires. This gives you a value "averaged over all possible futures weighted by their respective probabilities".

Most of those math models try to extract "implicit" information from the market...

Implicit information of a model flows from the decision-making structures (schemata) of the model based on the valuation and privileging of the total input stream from what is being modeled.  Baldly, you only see what you're looking for.  

In a mathematical model the problem is compounded¹ by the assumptions of Set Theory as applied in Probability and Statistics.  In the former, a pre-model decision is made to toss all 'unlikely' or low probability occurances into one variable if they are included in the model; in my experience these 'unlikely' occurances are ignored.  

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre