Bloodletting is one of the oldest medical techniques (and it is still used today). Justification for bloodletting has been linked to female menstruation and the balance of the four humors. The four humors (or four liquids/fluids in the body) are blood, phlegm, black bile, and yellow bile. Many ancient physicians believed that the humors needed to be balanced for a person to be healthy. If one had too much blood, he or she would not be well and the excess blood would need to be let out.
In order to do this, the physician would use an instrument with small blades which would slice the skin. Some of the bloodletting tools are pretty frightening.
As for the effectiveness of bloodletting, it is a common practice still used today. If it were not effective, it would not have survived until today. Today it is used in blood transfusions and (technically) when blood samples are taken.
As for its effectiveness in the past, based upon the "was" in the question, bloodletting was effective. Whether it was the balance of the humors or not, the removal of blood was known to cure some people of their illnesses (be it real or imagined). Think about bloodletting this way: if a person in the ancient world had a blood-blister, the blister would be opened allowing the blood to be let out.