Qualitative research is research that deals in things like feelings and emotions that cannot be reduced to numbers or statistics. This is in contrast to quantitative research, which investigates things that can be easily counted and subjected to statistical analysis.
With regard to the marketing of cosmetics, qualitative research might involve market segmentation. A marketer might look at the different ways in which various groups of people feel about buying cosmetics. They might try to determine, for example, if young teens feel different emotions when buying or thinking about cosmetics than women in their thirties. They might try to determine what sort of “feel” a makeup artist wants as compared to an ordinary person. All of these things are qualitative research because they have to do with feelings, not with statistical data.