The circuit diagram that you have drawn is a model of the system (battery and external resistor $R$) that you are considering.
If you did an experiment to measure the potential difference across the terminals of the battery $V$ (which is 10 V in this case) against the current passing through the battery $I$ your results would produce a graph something like this.
To model this arrangement you assume that you have a perfect cell of emf $10\,\rm V$ and internal resistance $r$.
Such a model will give you the same VI characteristics for the battery.
In terms of energy the internal resistance represents a loss of electrical energy produced by the electrochemical reaction within the battery when a current passes through the battery.
The workings of a battery are exceeding complex as can be judged from the fact that the model described above can only be used if the characteristics of the battery do not change with time.
The reason for this is that the "internal resistance" is not a resistor placed within a cell but rather convenient way of accounting for the complex processes occurring within the battery.
Contributions to the internal resistance will certainly come from the resistance of the metal conductors (which might change due to corrosion or formation of crystals/chemicals on them), the resistance of the electrolytes (which includes ion mobility which may change due to loss or change of composition of the electrolyte) and the resistance of any separators used within the battery (which are supposed to be porous but the pores may be clogged up).
Then there are changes due to the rate of the electrochemical reactions within the battery.
So as a battery delivers current many things happen within the battery and these may or may not be reversible and in the real world the internal resistance of a battery depends on many factors including time and temperature.
If you want to know more as to the workings of a battery and hence what might contribute to its internal resistance you need to start looking at specific types of batteries.
As a start you may find this link useful or this one?