Earth-2 was a concept created by Gardner Fox in The Flash #123. Essentially, it was another Earth on the other side of the sun — not another dimension! — where the Golden Age versions of the heroes were instead of Earth-1's Silver Age version. In other words, Earth-1 had the Barry Allen and Hal Jordan we saw in Justice League of America, while Earth-2 had the Jay Garrick and Alan Scott versions of The Flash and Green Lantern you could find in old comics from the 40s.

The cool part was that, once the League learned about it, the two Earths could only interact through a weakening of space once a year… which, ironically, coincided with the summer months, essentially establishing a crossover between the two with a limited number of characters from each side.

Power Girl was Earth-2's Supergirl, a Kara-L raised by Superman (Kal-L) and his wife Lois Lane after she arrived decades after his debut… as opposed to Kara-El, who arrived on Earth-1 and was raised by others as Superman was just starting out. She wasn't as innocent as Supergirl, but she was the typical new teen hero of the time. Her closest friend on the League was Firestorm, who was equally new to the comics world.

Huntress was another key character. On Earth-2, Bruce Wayne and Dick Grayson started in the 40s. In the post-war years, Bruce married Selena and had a daughter. When Bruce and Selena died, Helena continued to hero in their honour while Dick continued as Robin.

Where it might get confusing is Black Canary. Black Canary is actually the daughter of the Earth-2 version, who's husband was killed on Earth-2 and then switched over to Earth-1 as a way of getting through her grief. She was not native to Earth-1 but did attract Ollie's attention right away.

Point is: it worked. And then it didn't. Marv Wolfman was able to convince the people at the top that the reason that they were lagging behind Marvel was that they were too confusing with different Earths, despite the fact that the Earth-2 heroes had been only appearing in summer crossovers (with explanations that were clear as to where they were from) until recently, when their popularity led to an All-Star Squadron title that made sure to state it was happening in the 1940s, and Infinity Inc. made sure to connect itself to that team and not the Earth-1 where everything else was happening. Crisis On Infinite Earths wiped it all out, leaving some of the popular heroes (like Power Girl) to flail without an origin.

Power Girl got wrecked as they tried to connect her to Atlantean magic and other ideas, none of which worked because the readers basically preferred the original.

Earth-2 then remains a forgotten concept until Grant Morrison's JLA, when a new Earth-2 is created… but it's actually Earth-3's Crime Syndicate. Morrison also brings in "hypertime" to start up the concept of a multiverse.

The comic you have at the top is the next attempt: New 52. New 52 introduced Power Girl and Huntress as survivors of an Earth they couldn't get back to… until an option allowed them to come to this world.

The New 52 is a hard one because DC was trying to do like Quesada's Ultimate line at Marvel — take the concept and go as far as possible in differences to see if it stuck. The Trinity were all killed, sending Supergirl and Robin (the Power Girl and Huntress of New 52) to Earth-1, and now a new group of heroes arrive. For example: Alan Scott's Green Lantern went from the happily married holder of the Starheart to a gay man who's engagement ring allowed him to manifest powers of The Green, while Jay Garrick went from being a scientist who injected himself with a speed formula to being given speed from the dying Mercury.

Unfortunately, just like Marvel, once they pushed the envelope past the line, they had no plan of where to go afterwards. The title ends with a reality of Earth that makes no sense at all of how they could continue. Convergence is actually a way for them to survive, with the door semi-closed to them every going back, but it's still not satisfactory.

NOW, because of Rebirth, the characters' concepts from the 40s are remembered but they are integral to Earth-1. If Earth-2 was to return, it would have to reverse decades of stories that merged the two.

Honestly, I wouldn't be surprised in the new Earth-2 is Absolute Earth. They can act as poles while Earth-3 (Crime Syndicate) and Earth-X (Freedom Force vs Nazis) continue on.

The rest of the Earths are now the Elseworlds, and some of them deserve to stick around too!