In any situation where something can't be measure Quantitatively.
These situations are very numerous in the Psychological sciences where things are rarely reduced to numbers.
Emotions are a good example. Understanding or building a test on what a person is feeling needs to be done in a qualitative way.
Possible Brain Scan Scenario:
What Emotions do you feel when viewing this picture?
The Researcher would not only collect data on the subjects qualitative answers, but also he would chart down qualitative and quantitative data about the brain scan itself.
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Some variables in the data set might be qualitative, others might not. For example, if one were to sample newly arrived immigrants to Toronto, Canada and create a data set of information about them one could include both qualitative and quantitative data. One might measure each person's height which would be quantitative, and observe each person's eye colour, which would be qualitative.
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Qualitative means what is it while quantative means how much is there. Some examples of qualitative data might be whether a solution is of copper or iron or if a compound is formed with nitrate or carbonate. Quantative data could be the concentration of a solution or the mass present in a sample.
It is numerical information about some characteristic. By contrast, qualitative data might be something like the colour of your eyes, or the name of your maths teacher.