Put simply, it's about money. Colleges get so many applications that they need a way to weed out some of them. The bigger and "better" the college, the bigger this problem is for them. Colleges have decided that a standardized test such as the SAT (or ACT) is the answer to this problem.
Consider the hypothetical situation of "highly competitive" Brainiac University: they have room for 2,000 freshmen, but they receive 8,000 applications. How do they get through all of these applications? How can they say "Oh, I’m sorry…" 6,000 times as inexpensively as possible? They use standardized test scores as a cheap and easy way to differentiate candidates. A 95 average at Northern Hopps High and at Henry Edward Dudonk High may or may not mean the same thing, but the SAT helps them compare people from very different educational backgrounds on what some consider to be a "level playing field."
At upper-tier universities, computers can be programmed to make a large percentage of the admissions decisions primarily on the quantitative aspects of your application. Computers do things way cheaper and faster than humans do. So "Brainiac U." can fill most of its incoming freshman seats without overburdening the admissions office, not to mention the accounting office.
Who takes the SAT? When can I take the SAT?