Here is a screencast showing 2 simulations I made to illustrate energy states (often also called microstates).  Open any book on 
statistical mechanics and you'll see a formula like this (for the 
Boltzmann distribution),
and, perhaps, a figure much like this.
But what are these "energy states" and 
ε's exactly? Hopefully the screencast and associated simulations, which you can find 
here and 
here, will help make this clearer.
About the simulations
If you want to play around with the HCl simulation, note that you have to reload the page if you want to change the translational motion.  This simulation is made with 
Jmol.  The molecular dynamics simulation of butane is made with 
Molecular Workbench.