A double blind experiment is one in which a specific technique is used to make sure that the researcher does not influence the subject to pick one choice or another.
Take for example a taste test for which soft drink people prefer. In a double blind test, neither the researcher nor the person drinking would know which soda is which. That way, the researcher would not be able to give hints (either on purpose or accidentally) as to which one the person drinking should choose. This is why the study is "double" blind -- both the researcher and the test subject are "blind" because neither of them knows which choice is which.
Perhaps a more scientific example would be in a test for a medicine. If a doctor is giving some patients a real medicine and some a placebo, the doctor must not know which is which. If they did know, they might act differently when doing it and that would tip off the patient as to which thing they were getting. This would spoil the test.
A double blind study is one where neither the researcher or the patient/client is aware of the placebo or the tested item.