[Jain, Ch. 17]
This is a popular method to begin analysis of a problem with many factors.I always suggest this to students. It is easy to use and to analyze. That's because you consider only two levels for each value: high and low.
After performing a 2^k design, you can judge which factors to explore further, and then design further experiments.
Often the effect of a factor is unidirectional: the response variable either continuously increases or decreases as the factor level is increased from minimum to maximum. In this case a 2^k design is highly effective.