Quantitative results are measure quantity, which means they are numerical. If you are taking doing a survey of people's political positions as conservative or liberal, you will have quantitative results, for example, that 43% of the people surveyed called themselves conservative and 57% of the people surveyed called themselves liberal.
Qualitative results measure quality, which means that numbers are not involved. An example of a a quantitative result to a survey might be a series of responses explaining what the people surveyed did or did not like about a particular product.
Sometimes results include both qualitative and quantitative results. A survey in which people were asked to state whether or not they liked a product and were also asked to comment on what they liked or didn't would result in qualitative comments and quantitative results in raw numbers or percentages.
Generally speaking, it is good to have qualitative and quantitative information before making a judgement or a decision. Numbers alone do not necessarily tell a story, while qualitative results do not tell us about numbers that could be very important.