Not all heroes start with an origin story, but the good folks at DC felt that a guy who could breathe underwater and command sea creatures probably needed SOME explanation. Here, in an excerpt from the Dec, 1941 issue of More Fun Comics #73 we see Aquaman briefly explain his origin to a mystified sea captain:


It is interesting to note that Aquaman is not the first water-breathing superhero. That honor goes to Namor, The Sub-Mariner, who debuted in Marvel Comics #1 October, 1939. Aquaman's original origin is significantly different from the Sub-Mariner's, as the Sub-Mariner is the son of a human sailor and an Atlantean princess. However, in 1959, following the makeovers received by Green Lantern, Wonder Woman, Flash, Hawkman and The Atom, Aquaman was refitted with a Silver Age revision to his origin which has a few familiar concepts:




I particularly like how he seems to have always worn an orange shirt and green pants.
One of the great things about Aquaman is his utter lack of a Secret Identity. He doesn't even have a name other than Aquaman until 1959. And even when he's revealed to be Arthur Curry, it's not like he's masquerading as , for instance, the bumbling second mate on a Coast Guard cutter or something equally inconvenient. He's just Aquaman. He lives in the sea. Being Aquaman is apparently a full-time job.
By the late 1960's, Aquaman was moved from just being a very helpful guy to being the king of Atlantis. I've always felt that Aquaman , forgive the expression, "jumped the shark" at that point.
Heavy hangs the head that wears the crown, as they say, and by the 70's Aquaman became a very heavy cat. Always worried about pollution and the good of Altlantis. He was no longer the happy-go-lucky superhero stopping pirates and delivering letters to remote islands. He had a wife and a baby son and tons of responsibility. And his villains started getting more and more aggressive.
Honestly, when I read the Silver Age Aquaman, I become nostalgic for a simpler time (in comics, anyway) where superheroes were pure adventure and no writer would have EVER thought of killing off a superhero's infant child just to boost readership.

R.I.P Aqua-Baby.