The distinction here is an important one, and goes well beyond the narrow view of qualitative as “open ended” as in an open-ended survey question. Rather, studies that are qualitative in nature generate data about behaviors or attitudes based on observing them directly, whereas in quantitative studies, the data about the behavior or attitudes in question are gathered indirectly, through a measurement or an instrument such as a survey or an analytics tool. In field studies and usability studies, for example, the researcher directly observes how people use technology (or not) to meet their needs. This gives them the ability to ask questions, probe on behavior, or possibly even adjust the study protocol to better meet its objectives. Analysis of the data is usually not mathematical.
By contrast, insights in quantitative methods are typically derived from mathematical analysis, since the instrument of data collection (e.g., survey tool or web-server log) captures such large amounts of data that are easily coded numerically.
Due to the nature of their differences, qualitative methods are much better suited for answering questions about why or how to fix a problem, whereas quantitative methods do a much better job answering how many and how much types of questions. Having such numbers helps prioritize resources, for example to focus on issues with the biggest impact. The following chart illustrates how the first two dimensions affect the types of questions that can be asked: