As someone who bummed around the high levels of the academy for years as research staff, let me tell you what it means. It means lots of stress (and has been described as drinking from a firehose), and lots of ego, and a more prestigious brand associated with your diploma, exactly comparable to having a Gucci purse instead of one from Banana Republic. It does not mean more capable students, more capable faculty, or better resources for an individual undergraduate.

Studentry plateaus in intelligence and ability at the level of a decent state university. Faculty plateaus at a lower level of prestige than that. The prestige is useful for only two things: marrying into privilege and getting jobs with certain prestigious firms in management consulting and finance. If neither is important to you, then there is no reason to spend $180k on MIT instead of $60k to $80k on your state school. Or $5k on four years of tuition at the EPFL in Switzerland, which is as prestigious as MIT or Caltech. (Numbers are tuition and fees, but not cost of living, for four years. State universities are in-state tuition. EPFL is international student tuition.)

And if you're interested in engineering and lucky enough to live in California, Georgia, Colorado, or Alabama, you have a state university that, in engineering, is more prestigious than MIT.