WARNING: The following article has SPOILERS For the Supergirl episode "Battles Lost And Won"
Supergirl's Season 3 finale, "Battles Lost And Won", offered a number of surprising shifts to the status quo of the series. None was quite so surprising, however, as the final scene, in which an apparent clone of Supergirl was found walking towards a Russian military base on the Siberian border. What this could mean is anybody's guess, but previous Supergirl stories from the comics do offer several possibilities worth consideration.
The Supergirl clone was apparently created during her battle with Reign - the main villain of Season 3. Rather than killing Reign, Supergirl used a piece of Harun-El (a unique Kryptonian rock with strange properties akin to Kryptonite) to force Reign into a psychic realm. Harun-El had been shown to have the power to split two souls that had been joined together, as in the case of Reign and Samantha Arias - a woman who had been forcibly used as a host for the spirit of Reign. The episode ended with Samantha free of the curse of Reign but Supergirl's actions having apparently created a doppelganger of her own, who manifested in Russia.
Several Supergirl stories have dealt with Kara Zor-El facing her own dark side, such as when Kara became more uninhibited after being exposed to Red Kryptonite in the first season episode, "Falling." There have also been stories in the comics where she was exposed to Black Kryptonite - a form of Kryptonite that creates evil clones of the Kryptonians exposed to it. It is possible that Harun-El is being used in place of Black Kryptonite for the sake of the storyline in Supergirl, given that all the naturally occurring Kryptonite on Earth is supposed to have been destroyed.
The Russian location suggests something much more complex than a mere battle between evil twins, however, and it is worth noting that Supergirl has some surprising ties to Russia in the comics. In The New 52 DC Comics universe, Kara Zor-El's rocket landed in Russia and Kara's first exposure to the people of Earth was being shot at by Russian soldiers. In the alternate reality of DC Bombshells, Kara Zor-El was raised by Russian farmers as Kara Starikov, and became a protector of Russia during World War II, along with her adopted sister Kortni Duginovna (a.k.a. Stargirl). There is another famous Elseworlds story, Superman: Red Son, based around the idea of Superman being raised as a Russian superhero and changing the course of world history.
Another interesting possibility worth noting is that Kara approaches the soldiers apparently naked except for a sheet wrapped around herself. This is how Supergirl first appeared when she was reintroduced into the post-Crisis DC Universe in the pages of Superman/Batman. There was a major storyline which followed her introduction, built around Batman's exploring the possibility of this Kara Zor-El being an artificially created being who had been programmed to kill Superman.
The Supergirl series has hardly been shy about tackling touchy social issues, devoting entire episodes to gun control, gay rights and religious extremism in the past season alone. Given that, it does seem likely they may be pushing to see a Russian-controlled Supergirl pitted against Kara Zor-El in Season 4, as a parable for the increasing hostility between the Russian and American governments and the beginnings of a new Cold War. Should this come to pass, it will be the greatest battle of champions between the two nations, since Rocky Balboa faced Ivan Drago.