That scene is one of my favorites too.
First of all, for such a brief scene, the dialogue does so many things. It establishes Bruce as intrigued by Selina, establishes Selina's background, worldview, and shows her at the prime of being a con artist, it works as a "warning" foreshadowing the coming storm, and has several extremely memorable, quotable lines ("I'm adaptable": classic Catwoman, and "There's a storm is coming, Mr. Wayne", which establishes the tone of the whole movie and references both Begins and a Tale of Two Cities).
Then, meanwhile, there's the symbolism of the masks everyone is wearing, the symbolism of her pearls, the fact that Bruce does not need a cane when they're dancing.
And from a technical standpoint, they lit the scene extremely similarly to the ballroom scene in Eyes Wide Shut, Kubrick's last film and one of my favorites, which also features masquerade masks and even has a few of the same themes as this film. The music reminds me very much of the waltz music from that same scene. And the editing, with the jump cuts in between their dialogue, is really cool, and unique for a Nolan film.
Plus, there's the awesome bits before and after with Bruce deactivating the cameras of the paparazzi after they get excited about his return to the spotlight, and Selina stealing Bruce's car. And the fact that Miranda is holding a charity ball really reinforces the whole "doing what is necessary to save the world", which both highlights what she keeps telling Bruce he needs to do, as well as her, er, other motives.
And, of course, this entire scene also recalls the masquerade Selina/Bruce dance in Batman Returns.
