What he means to the universe
Captain America is unequivocally a hero (as mentioned here, here, and here) to the people, but equally important is the force he’s been in the universe as it pertains to heroes. 
As I mentioned here, the Avengers called on him to lead in what could have been a very volatile point in Avengers history, with the introduction of three reformed villains, two of whom were mutants. This had the potential for disaster but, as one would expect, Cap handled it and turned it around, eventually molding some of the biggest Avengers in history in Hawkeye, Quicksilver, and Scarlet Witch (Hawkeye, particularly, is viewed as one of the best Avengers, despite his penchant for whininess and running out of arrows).
So great, he led a team. Way to go. 90% of heroes in this universe have led some team or other. What makes him so great? First, shut up. Obviously he’s great. Second of all, this isn’t just a team, this is the Avengers. And this wasn’t when they had a rep as the biggest and baddest, this was their second team. Iron Man and Thor were gone, Giant Man and the Wasp were out for a bit (big loss) and the world was at its peak of hating mutants and whiny villain-turned-hero archers (they were a specific bunch back then). And Cap turned them around. He didn’t even make a big deal about it! He just did it! What’s most telling, of course, is that no one even questioned this idea, not for a moment. Of course Cap will lead them and raise them and train them and make them respectable. He’s Captain America, the living legend.
There are all kinds of heroes who have problems with other heroes, for one reason or another. Daredevil is easily annoyed, Iron Man doesn’t deal well with new people (or is racist, Triathalon would have us believe), Luke Cage bitches and moans about every single person in the world because HE’S so great (P.S., why does everyone love Cage? I totally need to know), most heroes have a love-hate relationship with the X-Men, Spider-Man pisses off a good percentage of the hero community and every single hero hates the Punisher. Cap, however, is nearly universally respected, if not universally loved. Everyone references the fact that, if Cap’s around, not only do they have a good chance in a fight, they probably have the moral high ground too. That’s why Maria Hill wanted to put him down early in Civil War, knowing that he’d give the boost that the anti-registration forces needed (also a big part of why she is SO very unlikable). Even a certain percentage of villains draw the line at going against Captain America. Where everyone else in the universe has some dark aspect to his or her past from which he or she is trying to hide or move away (Iron Man’s alcoholism, Ms. Marvel’s alcoholism, Spider-Man’s inability to save his uncle, Black Widow’s shadowy past, Spiderwoman’s shadowy past, Giant Man’s wife-beating, etc.), Cap’s biggest struggle is dealing with a new and foreign time period and losing all his old friends. He’s never regretted a side of a battle he was on, never lost faith in an issue and never stopped being a hero, not even for a moment. Even when Brubaker took the reins and Sharon Carter confronted him about his acting more irrationally than normal, the incidents she’s referring to are when he killed terrorists trying to set a dirty bomb off on a train in New York City instead of risking losing the train and saving their lives. Kind of a different deal than Iron Man flying around in the most advanced weapon in the word while totally wasted.
After Siege, the world was seemingly irreparably damaged, the superhero community coming off its lowest blow in years. Who did the president turn to? Steve Rogers. Not even as Captain America; the president asked Steve Rogers to take control. In a world that has such control issues and such huge threats, to ask a man, an above average man sure but still just a man in the end, to try to right the ship takes one hell of a man. And the world knew they had it.
