Stepper motors are designed to move in specific increments; these increments are called "steps". For example, a common standard is for 200 steps per full revolution. Microstepping is a method to send signals to the motor to move only a fraction of a full step at a time. For example, if a motor has 200 steps per revolution and is microstepped 1/16, then effectively there are 3200 small step movements (microsteps) per revolution instead of 200 larger ones. This makes the motion of the motor much smoother and more precisely controllable, at the cost of decreased holding torque.

Here are is a good references for stepper motor theory: http://users.ece.utexas.edu/~valvano/Datasheets/StepperMicrostep.pdf

And Wikipedia has a good overview as well:
https://en.wikipedia.org/wiki/Stepper_motor

Additional Information:


Additional Information:
Therefore, the difference in 128th and 64th microstepping is increased resolution and smoothness for 128th microstepping, at the cost of decreased holding torque.