In sociology, (and in other social sciences) the terms “quantitative” and “qualitative” refer to two different approaches to doing research. Sociologists use one or the other, or a combination of the two, while conducting research.
Quantitative research is research that has to do with things that can be counted and statistically analyzed. Quantitative researchers tend to use methods that can get them large amounts of data because large amounts of data are needed to make quantitative methods be statistically significant. Therefore, quantitative researchers will do things like “crunching” numbers from census data or conducting mass surveys. These sorts of methods get them a great deal of data which they can then analyze statistically.
Qualitative research is done on a much smaller scale. Such researchers want to gain a deep understanding of any particular issue. They do things like conducting one on one interviews or participant observations as a way of accomplishing this. For example, a qualitative researcher seeking to understand the impact of race on poverty may conduct interviews with a relatively few poor people. By interviewing them, the researcher hopes to understand how their race has affected their economic conditions. A quantitative researcher investigating race and poverty would not do interviews but would look at census and other data to try to statistically determine the extent to which race (as opposed to other factors) causes poverty.
Again, there are researchers who use both, but quantitative and qualitative methods are the two different types of methods used in sociological research.