Qualitative and quantitative research differ from one another in the type of data that they accumulate. Quantitative data are things that can easily be counted and manipulated statistically. Qualitative data are more impressionistic and cannot be objectively measured.
Let us look at some examples of this. Since you are asking this in relation to marketing, we will look at examples from that field. Let us imagine that a “big box” retailer is thinking about moving in to a certain market. It might conduct quantitative research about the people in that market. It will do research to find out how many people are in the market, what the income distribution among those people is, what the age distribution is, what their ethnic makeup is, and other such things. All of these are things that can be measured objectively. Qualitatively, they might look at what it is that people want from a store. They might pay a focus group researcher to conduct in-depth talks with consumers from the area, trying to get impressions from them as to what attributes they admire in a retailer. This would be qualitative because those are things that are harder to put into numbers.