Well, a $200 million athletic budget for starters, which is ~ 70% larger than Illinois' IIRC, helps. Then add in some very deep-pocketed donors (like Steve Ross and others.) Also a large, adjacent metropolitan area, filled with alums who are rabid Michigan sports fans and not diluted to the extent Chicago is by other followings. (In Detroit MSU plays serious second-fiddle to UM.) Also, more than a century of largely uninterrupted football excellence and national profile.
It's a brand that perhaps got itself started w/o help from the university admin but in the slipstream of which the university has drafted effortlessly for many decades. And it's not just football. It's everything, all the way down to women's field hockey. It also helps to have a longstanding, charismatic coach like Schembechler (or Paterno or Hayes) who becomes a power center unto himself and inextricably linked with the brand.
My favorite Woody Hayes quote, from the '60s when a local journalist asked how he would respond to criticism from faculty that the OSU football program overshadowed the academics of the university: "I disagree. Ohio State is a university of which the football team can be justifiably proud."
Said the Professor of Military History (he actually taught that course every winter until he was fired in '79.) Finger, meet eyes.
But these are rare situations in which a tremendous brand is created and sustained over many decades. And OSU still struggles with a reputation of having mediocre academics. I'm sympathetic to FLIllini's argument. But I think it comes down to who's sitting in the President/Chancellor's chair and what issues and crises command their attention, rather than benign neglect. When you're struggling to fill holes caused by dwindling state funding, as our Presidents/Chancellors have been doing for a long time, you tend to want an athletics department that doesn't create more fires to fight. When you're sailing comfortably on calm seas with a following wind you have the luxury of focusing more broadly. When I was a student, Stan Ikenberry (as President) and Thomas Everhart/Morton Weir (UIUC Chancellors) were outstanding leaders. I've not been too impressed with many of their successors. Nancy Cantor, for one, was a train wreck.
As for Michigan, I recall that Lee Bollinger (now president of Columbia Univ) wrote an entire book about the importance of athletics to the U of M brand. I read it ~ 20 years ago. And Mary Sue Coleman, his successor, stated flatly that the football program was a tremendously important asset to the university. And indeed it is.