Positive statements in economics refer to those that are based on facts and science, while normative assertions are those that are biased by opinion. Some situations call for positive statements, but they are not always possible if insufficient data is available.
An example of a positive assertion would be stating the unemployment rate of a country at a given point in time. This is a fact-based statement with no opinion attached to it. An example of a normative statement would be saying that the unemployment rate is too high. This statement may or may not be true, but it is based on the thoughts of those saying the statement.