Team Galactic are the villainous team in Sinnoh. Unlike previous villainous teams, they plan to destroy the current universe with the power of Dialga or Palkia. Once they would destroy the universe, they would use their ultimate power to build a new one, having them be the ultimate god.
However, you have to stop them from achieving their goal of ultimate destruction. To do this, however, you'll have to release the three psychic legendary Pokémon from their headquarters, who will then be able to stop the two aforementioned Pokémon from destroying the universe. Once this is accomplished, you will have to battle many of Team Galaxy's commanders using your Pokémon. After that, you'll be able to catch the legendary Dialga, Palkia or Giratina.