Coaxial cable theory
The thing to realize is that all electrical phenomena are governed by Maxwell's equations, which describe the relationship between electrical and magnetic fields and how they affect each other over time.

However, in many cases, we can analyze circuits using what's called the lumped circuit approximation. This is a set of rules that can be derived from Maxwell's equations. These rules apply when the circuit is small enough that speed-of-light delays from one side of the circuit to the other are insignificant. Kirchoff's voltage and current rules are the main tools for analyzing circuits in the lumped circuit approximation. I think these cases are what you're talking about when you say you're familiar with "a normal 2 wire system" where "ac current just flows through the conductor". 

We start talking about transmission lines when we have a conductor (and return path) that are long enough that speed of light matters. To analyze transmission line propagation, we use a different not-quite-so-simple simplification of Maxwell's equations called the telegrapher's equations. The solutions to the telegrapher's equations describe the propagation of signals on transmission lines. A full description and solution of the telegrapher's equations is more than I can write here, but you can read more about them on Wikipedia, for example.

The gist of it is, as you've probably learned, energy is transferred back and forth between electric and magnetic fields. The important electric field is the one created by the potential difference between the conductors, which extends through the dielectric medium. Similarly, the important magnetic field is created by the currents in the conductors, but the field is actually found in the dielectric. In the telegrapher's equations the electric field effect is represented by a "distributed" capacitance and the magnetic field by an "distributed" inductance, which lead to our typical characterization of transmission lines by capacitance and inductance per unit length, which combine to give the characteristic impedance.