What is meant by a full abstract model of a lambda-calculus like language?
In denotational semantics, you want to be able to map each of your language terms to some object in your semantic domain or model. Now, it cannot be any arbitrary domain/model as you like, but, informally speaking, something that gives a good intuition about how the language works (its computational behavior).

Milner tried to formalize what this "intuition" should be and called it full abstraction. Formally, a model is fully abstract if all observationally equivalent terms in the object language represent the same object in the model. Equationally:
$$\text{if }  ⟦t_1⟧ = ⟦t_2⟧  \text{then } t_1 \rightsquigarrow t_2 $$
where $\rightsquigarrow$ represents observational equivalence. In case of lambda-calculus observational equivalence would be $\beta\eta\alpha$ conversions and $⟦\_⟧$ is the denotation function.

There are few papers that you might want to take a look at if you are interested in seeing some full abstract models of lambda like languages:


Plotkin's paper that gives a full abstract model of the lambda like language called LCF 
Mulmuley's paper gives a full abstract model of typed lambda calculus.
Hyland and Ong's papers give a full abstract model of PCF using game semantics