In science, the control variable is the one factor in an experiment that the researcher holds steady in an effort to isolate the effect that is being studied. According to About.com, it is also sometimes referred to as the "constant" variable.
Science can be thought of as a method for reducing or eliminating the preconceived notions of the human being doing the experiments. Fallacious reasoning, such as confirmation bias, can sneak into even the most careful researchers' work, as described by How Stuff Works in relation to Gregor Mendel's seminal work in genetics. Sometimes, the desire to achieve a certain result damages the search for objectively true answers. By isolating just one variable--the height of the pea plant, for example--and controlling for other variables, such as total sunlight or rainfall, a scientist is able to eliminate much of the random noise that would otherwise obscure the phenomenon under investigation.
Drug trials are perhaps the most well-known arena for controlled experiments. As the FDA explains, volunteers to test new drugs are usually assigned to different groups before being issued the experimental medicine. One group is known as the control group and receives only a placebo. Any improvements reported by the control group cannot have been due to the drug, and so can be used to eliminate the "placebo effect" from the test group's results. In this case, the placebo is the control variable.