Answer:
The purpose of having a control sample is the possibility of having something to compare the results of your experiment.
For example with medicine, the sample that received the medicine are in X state now, this has not enough information really, you need a control sample that is in a state Y, and now you can compare the states X and Y and see how your medicine really affects the patients.
Other example is how a substance X changes the color of something, if you do not have a control sample, at the end of the experiment you can't se the actual color change, so your really need a control sample.
The control sample is called the "zero" or starting point in an experiment.