What is the function, if any, of such large-scale "oscillatory" activity? Recently I read an argument that such activity is just epiphenomenal, that it has no biologically useful causal role. I am something of an atheist turned agnostic about the importance of such signals, so in what follows I try my best to step into the role of advocate for the claim that such oscillations have interesting functional consequences.
Let's consider a few experimental facts about such large-scale synchronous activity (not an exhaustive list!):
1. Neuronal activity can be directly influenced by weak external electric fields. These are known as "ephaptic interactions" in the literature. The question of the function, extent, and importance of ephaptic interactions (relative to synaptic interactions) is an open question that has received little attention. Google "ephaptic interactions" if you want to see some of the research that has been done. It could be that, for a neuron near threshold, an ephaptic signal may nudge it up into a spiking regime (or push it down away from threshold, making it less likely to spike).The second and third results mentioned are likely indicative of some very cool and interesting synaptic processing, which puts the first line of evidence in a unique class. Ephaptic interactions are the key for those who think oscillations actually do something. Unfortunately, there isn't a lot of good work on the role of ephaptic interactions in nervous systems.
2. The efficacy with which plasticity is induced in rat barrel cortex is synchrony-dependent. In the study from Diamond's group, more synchrony implied higher probability of inducing cortical plasticity with their protocol. Note in this paper they measured synchrony among spike trains using extracellular recordings, not LFP or EEG.
[Link to paper]
3. Gilles Laurent's group pharmacologically disrupted "synchronous oscillations" in the honeybee CNS and showed this disruption impaired behavioral discrimination of similar odorants (but not discrimination of clearly distinct odorants). Similar pharmacological manipulations have been done in vertebrate systems (see Buzsaki paper below).
Note these pharmacological manipulations are not clean, which makes it hard to interpret the results.
[Laurent paper] [Buzsaki paper]
My guess is that it will turn out that ephaptic interactions are important for the functioning of some parts of some systems, but settling which parts of which systems isn't a question that can be resolved a priori. Unfortunately, right now we are stuck mostly with correlation studies, which keeps the ratio of inference to data unacceptably high.
Stepping back from specific data suggesting that oscillations are important, Buzsaki's book Rhythms of the Brain is likely a good place to start to get the theist's side of things with respect to the importance of oscillations. I should admit I haven't read it, but only seen him speak and have read some of his papers, so caveat emptor. I can say his experimental work is wonderful, much of it driven by questions about the function of oscillations in the CNS, so his book seems like a natural place to start for someone interested in this question.
Irina A. Erchova and Mathew E. Diamond (2004) Rapid Fluctuations in Rat Barrel Cortex Plasticity. The Journal of Neuroscience, June 30, 2004, 24(26):5931-5941
Stopfer, M., Bhagavan, S., Smith, B. H. and Laurent, G. (1997). “Impaired odour discrimination on desynchronization of odour-encoding neural assemblies.” Nature 390(6655): 70-4.
Robbe D, Montgomery SM, Thome A, Rueda-Orozco PE, McNaughton BL, Buzsaki G. Cannabinoids reveal importance of spike timing coordination in hippocampal function. Nat Neurosci. 9:1526-33 2006.