Qualitative analysis refers to analysis without respect to amount in detail.
I.E.
You mix chemical A and chemical B, is there a reaction? Maybe a rough estimate of how much.
Quantitative Analysis is taking the same chemical A and B, knowing exactly how much you have, exactly how much you end up with, etc.
Example.
Is there lead in the water supply? Is a qualitative question. The answer is yes or no.
If there is lead in the water supply, how much? This is a quantitative question.