One usage refers to analysis or theories which only attempt to describe how things are, as opposed to how they should be. In this sense, the opposite of positive is normative. An example would be positive, as opposed to normative, economic analysis.
Another sense of the word positive is used describe things which are defined by construction, as opposed to things which are defined "negatively", by the absence of something else. Examples are positive and negative rights, or positive and negative liberty.