The PCs are special to one degree or another. The best way I can think of the illustrate the degrees is with examples from other media.
At a bare minimum, they're special like Indiana Jones, Han Solo in
Star Wars, John McClain in
Die Hard or the crew in
Star Trek: Deep Space 9 - extremely capable people whose capabilities happen to come into play at a significant juncture in their world's history.
A step up from these are special like the SEEDs in
Final Fantasy 8, the crew of the Enterprise in a mainline
Star Trek series, or most superheroes in mainline comics. They deal with world-shaking issues because they're not just extremely capable, they're widely recognized in their societies as the MOST capable of dealing with those issues; they aren't just elite officers, they're the crew of the flagship; they aren't just powerful mercenaries, they're the best fighting unit in entire the world. This rank also includes characters who, while not necessarily widely recognized, are SO superior (and proactive) that they shake the pillars of heaven by their own immense talent - for example, Conan, Batman or Hyuga Ricdeau.
A step up from these are special in having a destiny they and they alone can complete - the pilots (especially Shinji Ikari) in
Neon Genesis Evangelion, Paul Atreides in
Dune, Fei Fong Wong in
Xenogears, Anakin and Luke Skywalker in
Star Wars, or Neo (and Agent Smith) in
The Matrix. These characters may actually be "weaker" than class two elite characters, but at the end of the day they're the ones who decide the destiny of entire campaign worlds. Of course, as Anakin and Shinji's examples attest, that doesn't give them plot immunity - they can screw up (or, in theory, even die), it just means the whole campaign world will go to hell if they do.
I've run campaigns at all three of these levels and even some at mixed levels (though this can be very tough).