The purpose of an experiment is to scientifically determine the nature of reality with data. The purpose of statistically designed experimentation in industry is to use an understanding of inferential statistics and the process being investigated to design an efficient and economical experiment to determine the real effect of process variables on the process output.
For example, you may want to eliminate a defect that has plagued you for the past two years. A statistically designed experiment would combine the engineering knowledge that you have of your process and use it to design an experiment that had, say, 16 different combinations of process settings instead of 32. Using inferential statistics, you can determine the effect of process variables individually and combined together to try to pin down the source of the defect.
To see a numerical example, click here.