An index is a formula, not a portfolio. It defines which securities qualify, how they are weighted and when the list is reviewed. The S&P 500 weights its members by free-float market capitalisation; the Dow Jones Industrial Average, unusually, weights by share price.
Weighting decides what the number actually tells you. In a capitalisation-weighted index the largest handful of companies can drive most of the annual move, so the index can rise while the median member falls. Equal-weighted versions of the same universe exist precisely to show that gap.
Because trillions of dollars track these baskets mechanically, membership itself matters. An addition to a major index forces index funds to buy, which is why inclusion announcements move prices before the change takes effect.