The image is from Young and Freedman's University Physics with Modern Physics, Chapter 29 (Electromagnetic Induction).
The image shows a parallel plate capacitor being charged where the current through the plane surface is the conduction current $i_C$. However there is no conduction current through the bulging surface in between the capacitor's plates. The section is subtitled Generalising Ampere's Law.
What I am stuck with is why is there not a conduction current, $i_C$, in the region between plates and what exactly is the 'bulging surface' and it's function?
Apologies if the answers to these are fairly obvious, I am still getting to grips with this subject and am working through it fairly slowly.