These experiment designs are a result of the amalgam of two-level Factorial Designs and incomplete block designs. They offer an economical alternative to central composite and full three-level Factorial Designs by using a fraction of the Experimental Runs required for these latter types of designs. However, they do require three levels of each factor.
Since these designs contain no points on the corners of the space created by the upper and lower levels of the factors, they're especially useful when the corner factor-level combinations are impossible or prohibitively costly to attain. They should therefore be used when the user does not need to predict the response at these extremes.
More on Box-Behnken Designs: - http://www.itl.nist.gov/div898/handbook/pri/section3/pri3362.htm