In a nutshell, a control group is a group of subjects in an experiment, similar in all relevant respects to the experimental group, and submitting to the same conditions and changes except those specifically under investigation. The effect of the experimental treatment is assessed by taking the difference after treatment between experimental and control group on whatever measure is being used.
It is important that you realise that the above definition is not all encompassing and can be considered to be too simplistic. I've spent well over 40 years involved in experimental group studies and there are exceptions to the above definition. This is a complex subject that's sometimes dependant on the particular field of research.
Defining a control group as a "group that has nothing done to it" is incorrect ; a control group can indeed have something done to it.