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.