If you keep asking a person in different ways if they're always in the middle of a party or standing next to the wall, you'll eventually find out if they consider themselves to be introverted or extraverted. Likewise for the other traits. But, at their coarsest levels, people probably already have an inkling about those. (E.g. before you took the test, did you think you may actually be extroverted, feelings oriented, and sensing?)
I think when it comes down to it, we take these tests for the enjoyment we get in reading about ourselves later. (The Great Facebook Personality Quiz Epidemic of Ought Nine is the foremost recent example of this in action.) It tickles that part of our brains that says "Someone's taken the time to get to know me—I must be important!", even if that someone is really an algorithm. And it's that, combined with all of the parts that are "right", that allows us to overlook the parts that are vague, over-generalized, right-but-with-certain-caveats, or flat-out wrong.
I think when it comes down to it, we take these tests for the enjoyment we get in reading about ourselves later. (The Great Facebook Personality Quiz Epidemic of Ought Nine is the foremost recent example of this in action.) It tickles that part of our brains that says "Someone's taken the time to get to know me—I must be important!", even if that someone is really an algorithm. And it's that, combined with all of the parts that are "right", that allows us to overlook the parts that are vague, over-generalized, right-but-with-certain-caveats, or flat-out wrong.