High Level Understanding Q: What *is* a magnetic/electric field? Note: I have seen this question -> (What is a magnetic field) and would still like some clarification.
I have also seen https://www.youtube.com/watch?v=hFAOXdXZ5TM and https://www.youtube.com/watch?annotation_id=annotation_3566029675&feature=iv&src_vid=hFAOXdXZ5TM&v=1TKSfAkWWN0, and I believe I understand the implications of Special Relativity (on at least a basic level).
To help get at my confusion, I'll list off a few specific questions that might help orient the discussion.
The "electric field" is neither mass, nor energy- right? It's just a "force"? I'm not 100% sure what that means... does that just reduce down to "yeah, it's the exhibited behavior at a quantum level that we don't yet understand beyond that"- or is there some higher-level construction here?
Like, for example: is the vector field a big soup of moving electrons, the vector at that point referring to the average direction of electrons at that point? (So electrons would be constantly looping through this field, "bumping into"/"dragging around" anything with aligned/conflicting fields) Or is it some orientation of electrons/atoms at that point that has some net effect in rubbing against others? What is at that point that exerts the force there?
This could be paralleled to the "gravitational field" in that there isn't a "thing" at the place where the force is exerted- but I've heard that explained as a "bending of spacetime" which, while I won't pretend to fully grok is at least satisfactory in explaining how two things can interact with no interacting... thing... between them.
At the end of the day- it's all just not clicking for me. Any resources or explanation to help that click would be greatly appreciated!
 A: A field is a field: not a force. A force describes the effect of the field on a specific "object" (see below) coupling to the field. In the current state of research, quantum fields (such as the photon field for electromagnetism, see Virtual photon description of B and E fields) are fundamental structures that cannot be decomposed or explained in simpler terms. 
Now an "object" is itself made of interacting fields (see Which is more fundamental, Fields or Particles?). So your nicely put "how two things can interact with no interacting... thing... between them" confusion can be dissolved away by getting rid of the "thing" thing. There are only fields.
The one concept I see that is more fundamental than a field is spacetime, since a field is a distribution of values in spacetime. Spacetime is where the "between them" and "interacting" parts of the above quotation of yours take some meaning. But if spacetime is emergent (see How can space and time arise from nothing?), it is possible that this whole business of fields is even more intricated than it seems.
As you can see, looking for high-level understanding, as you ask, is first and foremost learning how concepts relate one to another, which involves studying physics in its own terms, where the relationships between the thinking, the math and the experiments have a very specific taste, different from mathematics or philosophy.
