Three separate characters have taken on the mantle of Superboy over the course of DC Comics' history. The name can refer to a young version of Kal-El/Superman, Superman and Lois Lane's son - either Jon Lane Kent or Jonathan Samuel Kent - or Kon-El/Conner Kent. Titans' version of Superboy is an adaptation of Conner Kent, who in the comics is a cloned version of Superman. To make matters even more complicated, Conner Kent himself has three different origin stories. When he was originally introduced in 1993, Conner was an artificially engineered metahuman clone of Superman. Then, Conner's backstory was retconned in 2003 to make him a human/Kryptonian hybrid created by Project Cadmus from the DNA of Superman and the hero's archenemy Lex Luthor.
In 2011, DC relaunched their comics line with The New 52, in which Conner's origin was changed again. In this continuity, Conner was still a clone, but this time he was created by Project N.O.W.H.E.R.E. in an attempt to replicate Superman's son Jon Lane Kent. This version of Conner features the barcode-like Superman symbol on his upper arm. In terms of powers, Titans' Superboy clearly has Kryptonian super-strength. In the comics, the character also has heat vision, X-ray vision and freeze breath, in addition to tactile telekinesis, which allows him to telekinetically control items he touches and fly.
As for how Titans' version of Superboy, Conner seems to be a hybrid of the New 52 iteration of the character and the previously established canon. Though the visual design is closer to the New 52, it's clear this Superboy was created by the genetic engineering laboratory at Cadmus. That said, how exactly Conner Kent was engineered - using what specific DNA - in the world of Titans remains to be seen.
Krypto the dog first appeared in the DC comics in 1955, where he was a companion for the young Kal-El version of Superboy. This version of Krypto was a Kryptonian dog, and he possessed many of the same powers as Superman while on Earth, like flight, heat vision, super strength and endurance, etc. And, similar to how Earth dogs have more acute senses of smell and hearing than humans, some of Krypto's senses were more acute than Superman's.
Though Krypto originally also possessed super-canine intelligence, making him about as intelligent as a human, the character has since been retconned to have average dog intelligence. The explanations for how Krypto survived the destruction of Krypton have also varied, and in one incarnation, the Superdog was created by Brainiac 13 in a villainous plot to defeat Superman.
Based on the Titans post-credits scene, it's clear Krypto has some superpowers - heat vision at least - but it's uncertain whether he was also genetically engineered by Cadmus or was simply captured by the organization. Still, we know the dog will be a faithful companion to Superboy next season considering the hero rescued him from captivity.
What Superboy & Krypto Mean For Titans Season 2
Superboy has been a member of the Teen Titans in the comics, so it's likely the character will eventually join the team on DC Universe's TV show, with his canine companion in tow. However, it's unclear when that will happen. Based on the Titans season 1 finale post-credits scene, and the brutal way in which Superboy took out the Cadmus scientists, the DC character could easily be introduced as a villain or antagonist for the main team in season 2.
That said, it's not yet known how Superboy's storyline will tie into the plot threads of the show's main characters. Rachel and Dick are wrapped up in Trigon's influence, while Gar is also loyal to Rachel, which may mean he extends that loyalty to Trigon. Elsewhere, Kory and Donna know that Trigon poses a very serious threat to Earth and the entire universe, putting them at odds with their friends. Adding in Superboy for season 2 will no doubt further complicate these character dynamics - but he may also be a key ally to have in the fight against Trigon.
With the introduction of Superboy and Krypto, Titans expands the number of DC Comics superheroes included in the series. Although it's not yet clear how exactly they'll fit into the storyline of Titans season 2, them being introduced via a post-credits scene indicates they'll be important to the show going forward. While that will no doubt make the series even more complicated, bringing these characters in also allows Titans to explore more Superman mythology and depict Kryptonian abilities. There's still a great deal we still don't know about this version of Superboy and Krypto, but the post-credits scene hints at an exciting season 2 of Titans.
Titans season 1 is available in its entirety on DC Universe; it will return for season 2.