Is this a good explanation for a start/stop/retain relay circuit?
When the start button is not pressed the motor stops. 


That is not what I see.  In your drawing, when the start button is pressed, one of the R1 contacts closes in parallel with the switch.  This contact maintains relay coil current even when the Start button is released.  When the Start button is released, the motor continues to run.  The motor stops only when the Stop button is pressed, interrupting the R1 coil current.