Mirror Mirror
When Midna is relating the history of the Twili to Link she describes the Twilight Realm as an "anti-Hyrule", in a sense a reflection of the light world. This is symbollised by the Mirror of Twilight, the only link left between Hyrule and the Twilight Realm by the goddesses: to get to the Twilight Realm from Hyrule, the characters literally have to step "through the looking-glass" and into their own reflection.
The most obvious way this manifests in Twilight Princess thematically is in the link between Zelda and Midna. The way the game is set up in terms of plotting obscures the identity of Midna as the eponymous Twilight Princess intentionally, to lead the player to assume that this is Zelda.
The two are juxtaposed in this way, so when Midna muses about the carefree youth she perceives Zelda to have had, you can assume she's thinking about the carefree life that she didn't have — she goes on to say that she shouldn't begrudge Zelda the circumstances she didn't choose, just as Midna no doubt did not choose the circumstances of her own upbringing. In terms of personality, Midna is much more hot-and-cold than Zelda, who is more reserved as a character, and Twilight Princess itself performs a subversion on the typically close Link/Zelda relationship by building a closer relationship between Link and Midna instead. Twilight Princess is also the first time that Zelda is depicted as the matriarch of Hyrule, maybe to set up part of this parallel with Midna.
Also reflected are the relationships between Midna and Zant and their respective Triforce-carriers. While Midna states that her people told a legend about the divine hero appearing as a beast, she expresses doubt initially that Link will measure up to the task, and places more faith in her own abilities and the magic historically created by the Twili than in Link. Conversely, Zant casts Ganondorf himself as a god. This refers back to the arrogance that had Ganondorf defeated and banished to the Twilight Realm in the first place and foreshadows his defeat at the hands of modest Link.
In the end, Zelda says it herself: "Shadow and light are two sides of the same coin."