The "parallel cuts" option will create tool paths that are parallel to each other. The direction of the cuts is defined by the two angles. The angles in x, y and in z determine the direction of the parallel cuts of the toolpath. Imagine slicing an apple: You can slice it with a knife parallel from top to down or from left side to right side. The pictures in the dialog symbolize how to set the desired cutting direction using the angles.
With constant X:
Note that 0 degrees in X, Y creates motions parallel to the Y axis (constant X).
Changing just "Machining angle in z" to 90 degrees creates tool paths parallel to Y axis. The X distance is constant
Changing "Machining angle in z" as well as "Machining angle in x, y" to 90 degrees creates toolpaths parallel to X axis. The y distance is constant
With constant Z:
Changing "Machining angle in z" as well as "Machining angle in x, y" to 0 degrees creates circular toolpaths. The Z distance is constant.