Microshifting is a way of using a pitch shifter to thicken a sound. The pitch shifter is set to shift by a very small amount (usually less than a third of a semitone). Usually the pitch shifter adjusts each side of a stereo sound by a different amount – for example, the left channel might be shifted down by 15 cents and the right channel might be shifted up by 15 cents. Sometimes a very short delay (less than 50ms) is also added to the pitch shifted signal.
When the stereo pitch shifted signal is mixed with the original sound, the sound becomes thicker and wider. This is sometimes used on vocals or lead instrumental parts (such as guitars or synths) as a way of making them bigger without using backing harmonies or longer reverb/delays. In a way, it simulates a unison recording (where the same part is played three times and all three takes are layered). Microshifting has an unique sound, however, because the degree of pitch shift and delay is constant, whereas a unison performance will result in constantly-changing pitch and timing differences.
Microshifting is often used as an alternative to reverb in situations where a sound needs to be more diffuse but without the wash from a reverb tail. Because microshifting has a distinctive sound, it won’t be always be appropriate. It’s used commonly in pop music – especially modern energetic pop which often does not have much reverb. The best way to decide if it’s useful for you is to simply try it.
As a side note, many pitch shifters have a much wider range of control, and also have a feedback feature. This allows them to be used for outrageous special effects.