Many students have a difficult time understanding capacitors...I certainly did. How in the world can a circuit with a cut wire, where the capacitor is, have current flow? If you actually cut a wire in any other circuit the current dies! What is different about a capacitor?
The answer lies in the fact that a capacitor has a large area where charge stores, and therefore has an electric field that flows across the gap. You don't get this with the two ends of a cut wire. So there is something special about that electric field. Remember, there physically is no current flowing across the gap, only the electric field.
James Clerk Maxwell figured out the details back in the mid 1800s. This video will explain the details of what Maxwell discovered. He showed that, since it takes some time for a capacitor to charge up (think of our RC circuit derivations) or discharge, then the E-field is time dependent - it changes. This means there is a change in electric flux across the gap of a capacitor. Now, he knew Faraday's law said that when there is a changing magnetic field, then a circulating electric field is induced. Does it make sense that if an electric field changes a circulating magnetic field should be induced? Where have we seen circulating magnetic fields before? These are produced with electric currents in straight wires! This is Ampere's law. Could the changing electric flux of a capacitor act like a current in a wire? We call this the displacement current.
Turns out, YES! Check it out.