Resonance is probably very important in any good design which uses EM energy.  Tesla used resonance all the time...

What you have described is called an inductor.  An inductor is generally a coil wound around something. Sometimes an inductor is a coil wound in a circle. Anyway the setup you described sounds like two inductors side to side. Pretend you've got two of these.
(http://www.physics.sjsu.edu/becker/physics51/31_03_Inductor.JPG)

Okay so this is a full circuit for one inductor.

First notice, you are applying voltage from the battery to the circuit.  This voltage is called V, but it's not labeled. You can see battery is on the right hand side.  Imagine the wire is a pipe. I tend to think of the voltage as the "water pressure" in the circuit.

Second notice you are sending a current through the circuit.  This current is called i. I tend to think of the current as "how much water is flowing per second" in your circuit.

Third, and this is the interesting part... by sending current through the coil, you get a magnetic field.   The same kind of thing that comes out of a refigerator magnet. The magnetic field in the circuit is called B.

B is like a North / South pole. You can tell which way B will point by the "Right Hand Rule" and taking your hand, curling your fingers in direction of the current i , and seeing which way your thumb points.  Try it on the diagram. Curl your fingers in the direction of i (in the coil) and stick your thumb out.

 You will see your thumb points in the direction of B, the magnetic field.  (right to left, like this <---  )

And last, the swiggly thing on the lower left is just a variable resistor, it just limits how much current can flow through the circuit. Think of the resistor as a "smaller pipe" the water has to get through.

So what you have is an electromagnet (which creates magnetic field B). There is also voltage an current. Lastly, the coil is also an inductor (produces inductance) in the circuit.

Now for your idea, you are putting two of these side by side. What happens next will depend on how you hook it up. You wanted to play with resonance.  This is what I am doing as well.  Anyway, many different things could happen.  It will depend on how you drive your inductors. Are they in the same circuit?  Two separate circuits?  Are you sending in AC or DC?  What frequency?  There are many  variables you can change.  And there is plenty to explore.

So what can two side-by-side inductors do:
 Well one thing the set-up could do is send signals from one side and receive them at the other side.  (like a radio transmitter and receiver). Or maybe you create a double-strength electromagnet. Or maybe it levitates off the table because you discover a way to disturb the local gravitational field.   Anything is possible.

PS
Here is an official definition of resonance:

In physics, resonance is the tendency of a system to oscillate at maximum amplitude at certain frequencies, known as the system's resonance frequencies (or resonant frequencies). At these frequencies, even small periodic driving forces can produce large amplitude vibrations, because the system stores vibrational energy