An aberrant response is a response or answer that deviates from normal. For instance, in a personality questionnaire, a person may be asked the same question in several different ways. If one of these responses varies significantly from the other responses this could be considered an "aberrant" response.
For instance, these types of tests are used in marital and pre-marital counseling. By using repetitive questioning of this type it can assess honesty, and whether a person is being genuine in their responses or "playing good" to make themselves look better.