With respect to sociology, positivism is a way of looking at the world. It holds that the social sciences should be more like the hard sciences and that society can be understood through hard and fast rules that apply to it just as laws of nature apply to the real world.
Positivism holds that there are facts about the human world that are objectively true. These are facts that can be discovered and understood. This discovery can be accomplished through the scientific method.
Because positivists believe this, they believe that they can find absolute laws about how society should run. Positivists believe that they can prove that their theories about society are correct. Therefore, they can also use their scientific knowledge to create societies that will be superior to other societies.
Positivism, then, is a way of looking at the world that implies that social scientists can use science to change the world for the better. It holds that human society can be understood objectively and scientifically and that social scientists can find the right answers that tell us how our societies should be set up.