I speculated that Giratina might be the leading Pokémon of a third game if it was made. Either that, or the legendary pixies...
Anyway, whereas Dialga and Palkia rule time and space respectively, Giratina seems to be the Pokémon that connects the living world with the spirit world, or alternate dimensions in general. The text for the Town Map for the Spring Path / Sendoff Spring / Turnback Cave area:
"The fourth lake of Sinnoh that was kept secret."
"Beneath the lake's surface is a cave where dimensions are distorted."
According to the texts in the Canalave City, the legendary "pixies", Uxie, Mesprit, and Azelf represent knowledge, emotion, and will. Altogether, they represent life, and were responsible for the creation of life. They were created by the "Original One" (presumed to be Arceus), and were used to keep Dialga and Palkia in balance. They reside in the three lakes at the extrema of Sinnoh, Lake Acuity, Verity, and Valor.
Giratina's location is at this 4th lake, the Sendoff Spring, residing inside Turnback Cave. Inside the cave, there is a text that essentially says that the worlds of life and death are the same within that cave.
Giratina's connection to the mythology of Sinnoh is uncertain at this point. Is it possible that it was the final creation of Arceus after the legendary trio was created? And why is that whole area of the game a secret?
This isn't to say that Giratina is the Pokémon featured in the third game, should it exist. This is just mere extrapolation and speculation based on information that we know already from DP.