Economists tends to juggle between articulating facts and arguing what should be done with those facts. For example, one economist might say, "The American debt went up 3.8 billion dollars today, and we should therefore cut down on spending." Another economist might say "The American debt went up 3.8 billion dollars today, but those spendings are investments that helps America grow."
I used a very simple example, but you can see that both statements have two parts: the fact and the prescribed application of that fact.
The fact ("The American debt went up 3.8 billion dollars today") is the positive part of the analysis. It is a statement that can either be clearly proven to be right or wrong.
Each of the second parts of the sentence ("we should therefore cut down on spending" or "those spendings are an investment that helps America grow") are referred to as normative analyses. Those statements are opinions, and there are people who would both agree and disagree with that statement.
It's pretty simple, but there are a few things to keep in mind. For example, false statements can still be positive.
For example, "The American debt went up 3.8 billion dollars today, August 13" and "The American debt went up 100 billion dollars today, August 13" are both positive statements. One is right, and one is wrong. However, they are both positive because they can be easily proven or disproven.
Also keep in mind that there can also be disagreement over positive statements. One company may have calculated that there was a 3.8 billion dollar debt and another company may have calculated that the debt was 3.9 billion dollars- there can be a debate over whether good X, worth .1 billion dollars, should be accounted for. You can see how there is potential conflict over positive statements.
As you keep this concept in mind and potentially try to categorize statements into one analyses category, you will find there are a lot of grey areas. This is completely expected; as long as you understand the concept, however, you shouldn't worry too much.