Qualitative research is used to outline a problem or develop a method to approach the problem. Focus groups, in-depth interviews, uninterrupted observation groups are just a few of the qualitative research techniques most commonly used.
Quantitative research is a logical and data-led method that provides a measure of what people think from a statistical and numerical point of view. Data is collected through surveys (online, phone, paper), audits, and points of purchase (purchase transactions).
Ideally, businesses should use both qualitative and quantitative research since they provide different perspectives and will usually complement each other. If you can only afford one or the other, make sure you select the approach that best fits the research objectives and be aware of its limitations. Don't assume that doing more focus groups is a substitute for quantitative research or that a long survey will give you all the in-depth information you can get though qualitative research methods.