Full Step
This method of stepping the motor energizes both phases constantly to achieve full rated torque at all positions of the motor. If a stepper motor has 200 steps, one pulse equals one step. So, 200 pulses from the NC computer results in 360 degrees of motor shaft rotation. A unipolar stepper motor driver operating in full step mode energizes a single phase. A bipolar stepper motor driver energizes both coils to make a full step. See the images below. The first image is single coil full step operation while the second is dual core full step mode.
Half Step
The Half step mode energizes a single coil then two coils then one again. Alternating between energizing a single phase and both phases together gives the motor its higher resolution. A 200 step stepper motor operating in half step mode would have 400 positions, twice the normal resolution. However, the torque will vary depending on the step position because at times a single phase will be energizes while at other times both phases will be energized. Higher end drivers compensate by increasing the current through the single coil when a single coil is energized. This makes up for the loss in torque, making the half step mode very stable. See the image below. 
Micro-stepping
The micro-stepping mode is the most complex of all the stepping modes. That is why some stepper drivers only offer full and half step modes. Micro-stepping is when the current applied to each winding is proportional to a mathematical function, providing a fraction of a full step. The most common divisions are 1/4th, 1/8th, 1/10th, etc. However, there are some drivers that provide up to 1/256th of a full step. Micro-stepping provides greater resolution and smoother motor operation. This is very advantageous as it reduces the need for mechanical gearing when trying to achieve high resolution. However, micro-stepping can affect the repeatability of the motor.