Positive economics is the study of criteria of what is. Positive economists research economic phenomena that exist and create theories to explain why these phenomena exist. It is a pure, abstract science and is not very popular with contemporary economists, because economists are under pressure to research things that have relevance to policy. All positive economic statements must be demonstrable to be either true or false based upon hard data culled from the real world. For example, a positive economist might say predatory lending caused inflation in the housing market. This would be a positive statement, because the economist could objectively prove it to be either true or false. Positive economists avoid making value judgments.
Normative economics is the study of how things ought to be. Normative economists consider factors such as the social and ethical implications of economic phenomena and make arguments about the goals of public policies should be. You could say that normative economics is subjective, because not everyone agrees on what is economically fair and what the goals of public policy should be. For example, a normative economist might say that mortgage lending should be federally regulated so that banks do not make loans to people who won't be able to repay them, drive the housing prices up, then cause these people to lose those homes. This argument includes the value judgment that policy should prevent people from losing their homes and inflating the housing market.
Applied economics is the study of the relationship between positive and normative economics. These days, if you attend a postgraduate program in applied economics, you will probably be attending a program that focuses on a specific industry or commodity. For example, you could attend an applied economics program in food systems or trade. You might study economic theories, microeconomic analysis of a specific industry or resource, commodities, public policy or economics and law. While doing your research, you may substitute the variables of positive economic theory with concrete examples to come up with more specific conclusions in your work. You may also use positive economic theories to interpret real-world phenomena.