You can pretty much do the math on this one yourselves: swans = majestic, awesome, and noble. Plus, swans also = the people of Denmark. And since we already know swans = majestic, awesome, and noble, the transitive property tells us that the people of Denmark = majestic, awesome, and noble too. Ta-da!
First, there's the baby swan in "The Ugly Duckling" that doesn't realize how majestic it actually is until it grows up.
Then, Elisa's brothers in "The Wild Swans" are transformed into "swans, with golden crowns on their heads" (13.33). And that also sounds pretty majestic-looking.
The whole point of the short story "The Swans' Nest" is to compare Denmark to a swans' nest from which all these over-achieving swans fly out into the world: the Lombards and Normans (who conquered a good chunk of Europe), the Christian Danes who converted heathens to the cross, and finally astronomers, inventors, and sculptors who made their mark on the world.
So, Andersen is a fan of swans. And also of Denmark. But probably not of Da Bears or Da Bulls. Cuz that wouldn't make any sense.