Enterprise Architecture is a management tool that tries the to solve the problem of runaway complexity in an organization. This runaway complexity , also known as incidental complexity, is the enemy of organization, planning, and change management and can lead to solutions introducing different more severe problems, aka the butterfly effect or complexity theory. The way you deal with complex problems is to divide it into parts, this is good advice in every domain, not just EA. When dealing with a complex problem, like the ones you get in case studies and case interviews, you break a problem down into its component parts and then break the individual parts into their components and so on till you get to a level of detail where you feel comfortable analyzing the problem and recommending solutions.
To draw an analogy, software architecture is concerned with maintaining logical integrity and managing complexity within an application, enterprise architecture does the same thing, but at the level of the organization. Traditional Software Architecture uses models to describe parts of the solution in a way that encapsulates solution components, models like class diagrams, state diagrams and entity relationship diagrams are generally accepted software architecture diagrams. In EA, which operates at the organization level more abstract diagrams are used to encapsulate components, we have business architecture components, data architecture components, software architecture etc. The one thing that we have to be careful of in EA as well as other domains that use models is that a model is just that, an abstract view of an object, and as such is limited in how much it can help us in understanding the object and its interactions with other objects. One spurious way to solve this is to make the model as complex as the real object. This, however, defeats the purpose of modelling. The other way to deal with this limitation is to realize that models are abstractions and base all decisions on this understanding. In other words, lower your expectations of what a model can do and in turn what disciplines that rely on models can do.

