In education, at least, the concept of test validity has to do with whether the test truly measures what it is supposed to measure. In other words, if a test is supposed to measure a person's readiness for college and ability to perform once they reach college, does the test really do so?
Validity is an important consideration for those who are writing tests, whether it be the SAT or the evaluations that a teacher uses on students. In the case of the teacher, it is important that the questions on the test should truly cover the material that was taught in the class. In the case of the SAT, it is important that test questions should actually measure the student's ability to do college work (as opposed to measuring some set of prior knowledge that will not predict college performance).
Validity in testing, then, is the extent to which the test measures that which it is supposed to measure.