The Ivy League consists of eight universities that played together in an athletic conference. That seven of them are among the oldest and most influential universities in the country adds to the sense of prestige associated with them. But that is not a reflection on the value of an education from either Stanford or Chicago, which, in all honesty, is equivalent to any of the Ivys. As is true for several dozen universities and liberal arts colleges in the United States.
The other point is that there are only eight Ivy League schools, so like any other object that is widely sought after the level of prestige seems higher because of its scarcity. There are far more deserving high-achieving high school seniors in the United States than can be accommodated by the freshman class of the eight Ivy Leagues schools, so those who are accepted have basically won a lottery. Acceptance is based on dumb luck, not objective qualifications, because thousands of similarly achieving students were rejected. But if you were accepted then you were accepted into a class of schools of higher education that have a long pedigree of scholarly achievement and a strong network of powerful, accomplished and successful people.