What do the telegraph equations physically describe?

[aaaa202]

are derived in my book from the assumption that a wire can be cut into a lot of infinitesimal wires with a capacitance and inductance each.
Can someone explain to me what these physically describe? What is it that travel with the speed of almost light. I don't think it's the drift velocity so it must be the information that the fields have changed back at the battery or something like that. But that should mean that the waves they describe are equivalent to the ones predicted by decoupling maxwell's equations. If so, that is just weird. Maxwell's equations have assumed nothing about the wires and their self-inductance and capacitance, so it's just weird that they should give the exact same.
Also my book discusses how if you turn on voltage at the end of a circuit how the presence of a resistor later on the circuit is communicated via the telegraph equations. I want to understand this: Is it the bouncing of the physical electrons and their pushes against each other which communicates the presence of a change in the cable or is it the fields or something like that. Please just say as much as you can about this phenomenon because I don't really get it.

 

[Studiot]

The Telegraph equation is a special case of the Transmission line equation with zero series inductance and zero parallel leakage. It also resembles the heat conduction equation.

It describes an electromagnetic wave traveling in guided conditions, so yes, it is allied to Maxwells equations.

A change of characteristic impedance, such as a resistor, results in a reflected wave. That is how the resistor is detectable at the origin.

 

[aaaa202]

but why is it intuitively that the telegraph equations describes the same wave as the maxwell equations. Maxwells wave equations are derived by decoupling his field equations and then applying to them the boundary conditions involved with a medium. The telegraph equations looks at capacitance and inductance for small parts of a medium. It is just weird that these approaches are connected on such a deep level.
And can you tell me what it is that does a wave motion? Is it the fields of the electrons or the potential at different positions (as in the telegraph equations) or what is it?