Physical properties of transformers
About the core
Consider an inductor, and the magnitic field that it generates:

it creates loops all around the windings, with a direction given by the direction of the current (see Ampère's law).
If you put two inductors close to each other, the changing (Credits to Curd) field generated by one will induce (sorry for the pun) a current in the other one, with the proportion given by the number of windings (because of Faraday's law of induction). But this coupling will be limited to the portion of the field which falls in the area of the second inductor, which can or cannot be a limited portion of the total.
Using a core, you force whe magnetic flux over a closed path, and the great part of it will follow that path:

This translates in a higher efficiency of the coupling, as almost all the magnetic field is induced in the secondary, as opposed to the previous case.
What happens with two wires?
If you have a single ideal wire, it also generates a magnetic field, again described by Ampère's law:

Since this field is distributed through all the wire, it will be much weaker than using windings, because these have the effect to concentrate this field into the inner space (where is the core).
As for inductors, distance reduces the portion of the magnetic field that the wires share, and with it the power transferred. Note that with the core, in the ideal case in which all the flux is convoyed the distance doesn't matter, as all the flux is into the core.