The Forer Effect refers to the tendency of individuals to believe that generic personality descriptions are highly accurate when being told that the descriptions are tailor-made.
Forer famously gave a group of students a personality test. Then he provided them with an individual "analysis" which the students were supposed to rank from 0 to 5 (poor to excellent). The analysis read thusly (Thanks Wikipedia!):
You have a great need for other people to like and admire you. You have a tendency to be critical of yourself. You have a great deal of unused capacity which you have not turned to your advantage. While you have some personality weaknesses, you are generally able to compensate for them. Disciplined and self-controlled outside, you tend to be worrisome and insecure inside. At times you have serious doubts as to whether you have made the right decision or done the right thing. You prefer a certain amount of change and variety and become dissatisfied when hemmed in by restrictions and limitations. You pride yourself as an independent thinker and do not accept others' statements without satisfactory proof. You have found it unwise to be too frank in revealing yourself to others. At times you are extroverted, affable, sociable, while at other times you are introverted, wary, reserved. Some of your aspirations tend to be pretty unrealistic. Security is one of your major goals in life.
The average score was 4.26. It was then that Forer revealed that they all got the same text.
See Also #
Forer Effect at Wikipedia. Specifically, see Variables influencing the effect for additional criteria.
Derren Brown - Cold Reading at YouTube for a video of Derren Brown acting strangely, but demonstrating the basics of the Forer Effect.