Epic Space Opera Storytelling
For most of the films in the Star Wars series, George Lucas sticks with the basic form of storytelling: follow one or two plotlines that focus on a main character and then have them all come together at the end for an epic convergence of awesomeness.
In the case of Revenge of the Sith, we mostly have a third-person perspective of everything that's going on, with a few omniscient insights into the nightmares plaguing poor Anakin.
One of the narrative devices that Lucas uses to perfection throughout the film is cutaways in order to show different things happening in different places at the same time. It's like the old TV shows that used to announce, "Meanwhile, back at ___ ."
So, with this technique, we get a visually remarkable and symbolic moment at the end of the movie, where we see the divergence of Anakin Skywalker's fate and that of Darth Vader's. As Anakin is being assaulted by droids attaching new metal limbs and cybernetic devices, we cut back and forth to Padmé delivering their twins, Luke and Leia.
In this way, we witness the "birth" of three of the main characters—Luke, Leia, and Darth Vader—for the later movies, which is pretty dang clever storytelling.