Purposive sampling, also called intentional sampling, is just as the name implies: it is a sample chosen “on purpose” because those sampled meet specific criteria. This type of sampling is used in many qualitative studies to allow the researcher to identify small, specific groups to work with.
For example, I have written a lot about attrition from college, particularly doctoral students who complete their coursework but ultimately do not finish their dissertation. In the review of literature for my most recent article (Terrell, 2014), I found that most attrition occurs after students have been in their programs for 5 years or longer. Because I wanted to interview doctoral students who had dropped out after 5 years, I purposively chose 12 students who met my criteria and interviewed them. While I cannot be absolutely certain that the results of my student sample represents the population of students who left their doctoral programs, I do realize that this is probably the only way I could collect the data I wanted.