Terms in Propositional model:

There in first-order logic allows us to talking about properties of objects that the first job for our model (Δ, Θ) is to assign a meaning to the terms that represent objects. Here a ground term is any combination of constant and function symbols that Θ maps each individual ground term to a specific object in Δ. Because a ground term refers to a single specific object. Thus the meaning of subterms is usually independent of the term they appear in. 

The specific way the terms are mapped to objects depends on the model. At different models can define terms as refering to different things. Always notices that although father(john) and jack are separate terms but if they might both be mapped to the same object (say Jack) in Δ. Means i.e. the two terms are syntactically different but in this model they are semantically the same that is they both refer to the same thing! 

Means terms can also contain variables (e.g. father(X)) - these are non-ground terms. So however they don't refer to any specific object than our model can't assign any single meaning to them directly. Now there we'll come back to what variables mean.