As a comics reader since 1952, I remember the arrival of Supergirl in the life of her cousin, Superman. This incarnation has freely adapted concepts and characters from the DC mythos. The second season maintains the bubbly charm of the first while deepening the very relevant themes of inclusion v. paranoia against aliens and "outsiders".
David Harewood had apparently complained about the limited range given his character, the Martian Manhunter. This season J'onn J'onzz takes a front and center role in a complex subplot involving a female Martian here on Earth as part of an alien bar crowd who interact strongly with the regular cast.
Supergirl's adopted sister makes a dramatic decision in her long-suppressed search for love, broadening the series' approach to diversity and acceptance. Maggie Sawyer, introduced in the comics in the 80's, becomes a significant other as a smolderingly hot Latina with her own relationship issues.
The themes of family, betrayal, trust, and deeply manipulative games continue to get developed nicely. Cat Grant steps aside. I miss her acerbic, wise adult presence. However, Supergirl/Kara Danvers/Kara Zor-El maintains that sparkly cheerleader persona with the fists of steel and eyes of fire that worked magic in the first season.
Talk by the producers in an audio accompanying the "Supergirl Lives!" episode tells us that the series has claimed equal attention from adult men, adolescent lads, adult women, and adolescent gals. "Arrow" apparently captures more female audience, while "The Flash" attracts more males. "Supergirl" charms all four segments equally -- as anyone watching the show could guess.
Now that the show is moved to the CW, things are easier for the production company in terms of filming and budget. They can now cross-over to the other CW DC shows like Arrow and The Flash!
The series continues from the last season's episode where Mon-El lands on Earth. The second season deals with Mon-El's training, learning more about the Luthor's, Cadmus, and the Daxamites.
The character of Alex Danvers is now a lesbian (or bi-sexual), James Olson is now "just friends" with Kara, and Alex's father, Jeremiah, is alive and working as a double agent! The stupid part of the series was trying to include Trump-like dialog into the script ("Make Daxam great again!")! Liberals and Conservative fans of the show cringe on such lazy writing in trying to include "real world" events into this comic book show (where Lynda Carter is President and NOT Trump)!