Non-hierarchical theories are often nonlinear dynamical ones which focus on stable oscillatory or chaotic patterns found across the areas. Levels of organization and analysis refer to the different ways one can look at and theorize about the brain. Ionic transport across cell membranes would count as a lower level of organization. IPSPs, EPSPs, action potentials, and neuronal equilbrium are found at a higher level of analysis. We then find cell ensembles, areas, networks, lobes, and so on, up to the entire CNS considered as one unit.
Different theories operate at different levels.
Different phenomena require different levels of explanation. The trick in cognitive science and in brain studies in particular is to get the level of explanation right, for some things that we take as a weird and peculiar phenomena are only artifacts of looking at the wrong level for an explanation. This is where I suggested that the phenomena of psychological binding might fall. If we focus on a lower level hierarchical theory of visual processing, then binding looks completely mysterious. Contrary to what some have thought, though, this hypothesis does not require some higher level homunculus to discover which groups of neurons are firing in tandem.