Exactly the definition can be an operational one rather than the theoretical. As what kind of research one is doing and which environment one is looking for that set up will decide the suitability of the definition.As per books one can decide the enriched environment with reference to less pathology or disturbed background.It may be pointing towards healthy one or more positive one.
As a matter of practicality, it's an environment that is frequently modified and provides opportunities to learn.
As a conceptual matter, the gold standard, in my view, is an environment that affords the animal the opportunity to engage in all of the types of behavior that it would exhibit if it were not captive and were living in the typical environmental conditions for the species. This requires some knowledge of the behavioral ecology of the subject species, or at least closely related species from similar habitat types.
I fully agree with Michael Renner definition. I just would like to add that an environment which is overly loaded with stimuli (many conspecifics or other animals, a lot of changes in the objects arrangement and composition) might be very stressful (e.g. overcrowded) for animals. Thus even though such an environment might be classified as “enriched” it might not be an optimal environment for individuals to be raised and kept in.