A double blind experiment is a control group experiment where neither the subjects (if applicable), the people who have contact with the subjects, or the evaluator of the experiment know which subjects are in the control and which are in the experimental group.
This is desirable in many situations because it reduces one more source of researcher bias. If, for example, the doctor administrating a drug test knows which subjects received the drug and which received a placebo she is likely to treat them differently (paying more attention to the drugged patients and whatnot). If the researcher does not know then they are more likely to treat everyone the same.