The 3-position clean, as demonstrated here, is simply 3 cleans performed from 3 different starting positions. For example, from the floor, from the knee and from mid thigh.
This exercise has two key purposes:
Firstly, it forces the athlete to generate more power from a less advantageous hang position. This is also made harder given the fact that you are more fatigued as the set continues.
Secondly, it encourages the athlete to have a more aggressive turnover due to the limited pull. Cleaning from the mid thigh is a superb exercise to improve speed and confidence under the weight.