What is the purpose of a placebo group in an experiment?
In short: it is to counteract the 'placebo-effect'.
If you give a medicine to a person, the effect will be (in many cases) that the person feels better, even if there is no medicine at all.
This is called the placebo-effect, because doctors noticed, that patients felt better even if they gave them 'empty' tablets (placebo).
To make the experiment complete, not only should the patient be unaware of yes/no medicine, but so should the experimenters, or else the knowledge could be transferred to the patient (by the confidence/non-confidence of the experimenter, which might show unconsciously in his behaviour).
The knowledge about who gets the real thing and who gets the placebo is usually kept in encoded form, and only disclosed after the experiment is over.
This is called double-blind, and is the only allowed way to test medicines.