Several Factors are investigated at several levels but only a subset of the full factorial (all possible combinations) is run in a fractional factorial designed experiment.
It is appropriate to use this type of experiment design when there are many Factors and levels and it is impractical to run all combinations, or when higher order Interactions are unlikely.
A carefully designed fractional factorial experiment can yield useful information while greatly reducing the cost and time involved. For this reason it is a popular choice for Screening Designs. The disadvantage however is that many of the factor effects are aliased, requiring skill to unravel the hidden information.
Studies in Quality Improvement: Analysis of Fractional Factorials by R. Daniel Meyer - http://www.engr.wisc.edu/centers/cqpi/reports/pdfs/r016.pdf