Quantitative research is research that deals in things that can be reduced to numbers. It deals in statistics. This is in contrast to qualitative research, which investigates things like feelings and emotions that are less able to be put in numerical form.
With regard to the marketing of cosmetics, quantitative research might involve market segmentation. A marketer might look at the quantities of various sorts of cosmetics that are bought by people of various ages. Or they might look at the consumption habits by income. They might look at different patterns in buying by professionals and ordinary people. In all cases, it would be quantitative research because the researcher would be looking at hard numbers, not at things like emotions.