A case study (or case history) consists of an intensive, detailed description and analysis of a particular individual, group, or event. Such studies are frequently used in clinical and medical settings to provide descriptions and explanations of a person’s actions and experiences, as well as a prescription for the treatment of the individual’s problems (Runyan, 1982, p. 443). Information may be obtained by means of careful observation, interviews, psychological tests, or archival records.

Advantages

1. It is useful when the researcher is starting to investigate a new area or a rare phenomenon in which there is little information available. Case studies are a rich source of ideas and hypotheses for future research. 
2. It can also be used to disconfirm a generally accepted principle. Ex: In 1962, Eric Lenneberg reported the outcome of extensive tests over a five-year period on a young boy who was totally inarticulate because of an inborn defect of his vocal tract. Testing showed that he had normal and complete understanding of spoken language. This single counterexample was sufficient to invalidate the motor theory’s basic assumption - interpreting speech was dependent on the listener’s ability to produce speech.
3. Personality studies using the experimental method examine average or typical differences between individuals, whereas the case-study procedure provides a rich—that is, complex and integrated—view of the uniqueness of the person. It accomplishes this goal by describing both the consistencies and the inconsistencies of the person’s behavior, as well as the ways in which characteristic experiences are organized.

Limitations

1. Poor representativeness leads to limited generalizability. Because of the exclusive focus on a particular individual or group, the researcher has no way of knowing whether that individual is typical of people in general.
2. Case studies, by their very nature, do not permit the researcher to draw any conclusions as to causality. In a conventional experiment, the researcher usually has one or more specific hypotheses that are tested by the controlled manipulation of the specific variables of interest. Case studies do not permit careful control, thus it is impossible to identify a specific causal association.
3. The data obtained by the case history method may be retrospective or second-hand in nature and thus distorted by time. 
4. Even if the accuracy of such data can be verified, the conclusions drawn about the individual may reflect the personal biases of the investigator.

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Case study method gives an in-depth view of a single individual’s life or single event. This provides an opportunity to investigate phenomena which were hitherto not observed, thus helping in formulating or validating theories to explain such phenomena. It provides a complex, yet integrated view of a person. However, the focus on a particular case means the generalizability is limited. Also, the causality of the conclusions cannot be validated because of limited control on the variables. However, it is still a very useful method.

Sources:
Gale Encyclopedia of Psychology
Theories of Personality, Richard M. Ryckman (Click for eBook)