The SAT only matters within the spheres of college admissions and state testing. In those areas of influence, the SAT matters for the same reasons the ACT matters: both tests have been exquisitely designed over many decades to assess essential, research-supported prerequisites for student success in postsecondary education with extremely high levels of validity, reliability, and fairness.
Validity in a test describes the degree to which an exam measures what it claims to measure.
Reliability in a test describes the stability or consistency of measurement over time.
Fairness in a test describes its freedom from any kind of bias.
High school grades may be the single most important factor in college admissions, but these numbers are seen as subjective. Due to differences in the quality of schools, rigor of curriculum, and even grading philosophies of different teachers, no one can really trust the validity, reliability, and fairness of school tests.
The SAT and ACT, on the other hand, adhere to strict measures of impartiality and standardization. Every test taker follows the same rules and timing in the same general setting to work on one of a very limited number of test forms. College admissions offices value how objective these tests are and use SAT and ACT scores to put high school grades in context. The objective test scores help validate the subjective grades.
Taking the analysis one step further, we should recognize that the SAT qualifies as a norm-referenced tests, which means the test is designed to rank a broad population of graduating, college-bound high schoolers. Contrast this with criterion-referenced tests, which measure how much a test taker knows about a given topic or subject. Most exams in school are criterion-referenced, where each number or letter grade (e.g. A, B, C, D, or F) denotes a certain level of knowledge in a subject. SAT scores go beyond that measure to rank test performance along a bell curve, which helps admissions officers compare a large and highly homogeneous pool of applicants.