We know exactly what field lines are. They are a representation of the corresponding vector field. Maxwell's theory describes the electric and magnetic vector fields, and field lines are just one possible way to visualize these fields.Is it that no one knows the what field lines really are?
"Swapping gluons back and forth" may give you a satisfying mental image, but this statement is too vague to be an "explanation" of anything.What I'm driving at is analogous to stating the nature of the strong force is swapping qluons back and forth. To me that's satisfying enough of an explanation for now.
Photons.But there is no such explanation for magnetic force that I've ever heard. What particle mediates the magnetic force?