A controlled experiment is a study in which all variables but one is held constant so that the influence of one variable can be isolated. When conducting a controlled experiment, two different groups are required: a control group and an experimental group. The control group is not exposed to the external factor, whereas the experimental group is.
The reason for having both a control group and an experimental group is so that the factor which is being investigated can be completely isolated. All other possible influences need to remain completely unchanged and in the control group, the factor of interest also needs to stay constant. The goal here is to potentially establish causation.
For example, pretend you were interested in knowing whether or not there was a link between attending class and doing well on the final exam. In a controlled experiment you would have your two groups, each comprised of half the class. The control group would be of the students which do not attend class and the experimental group would be of students who do attend all classes. After the final exam, the average exam scores of both groups would be calculated and if the experimental group achieved a statistically significant higher overall average, this would signify that there is a connection between attending class and doing well on the final exam.
As the example highlights, a controlled experiment is good at narrowing in on one particular variable. The only downside is that in some cases controlled experiments, especially those which are scientifically based, are done in rather artificial settings, which may yield inaccurate results. In general, controlled experiments are commonly used in statistics and provide a useful method of analyzing particular variables of interest.
Image Credit: Education.com. (2014). Controlled Experiemnts. Retrieved from: http://www.education.com/reference/article/controlled-experiments/