What does "terms evaluated in related environments yield related values" means in the context of typing judgements? I am reading Theorems for free! by Philip Wadler which is a paper about how to derive theorems from the type signature of a function.


  Parametricity is just a reformulation of Reynolds’ abstraction theorem: terms evaluated in related environments yield related values.


What is an environment in this case ?
More generally, how do I interpret the statement in bold ?

I think I understand the parametricity thing correctly but somehow I cannot map this sentence to something more intuitive.
The environments are related not identical. The context of this statement is logical relations, as described e.g. here. A logical relation is a type-indexed family of relations which follows the structure of the types (in a way I won't elaborate on). If for each type $\tau$, we assign a (binary) relation $R[\tau]$, then given $f:\tau_1\to\tau_2,x:\tau_1\vdash f\, x : \tau_2$ when $R[\tau_1\to\tau_2](f,f')$ and $R[\tau_1](x,x')$ we can ask if it is the case that $R[\tau_2](f\, x,f'\, x')$. This is what it is referring to in "terms evaluated in related environments yield related result".