The distortion world is basically a parallel world
The Distortion World is said to be another universe or world parallel to the Pokémon world. Two gateways to it have been known to exist: one opened at the top of Mt. Coronet on the Spear Pillar, and the one present in Turnback Cave.
The world disobeys the normal laws of physics, creating an effect similar to the art of M. C. Escher: time is said to not flow and spatial relations are shown to be irregular, allowing the player to walk and Surf on walls in any direction. Trees and rocks can simply grow out of the ground and then disappear. The player is able to go up a waterfall without having the move Waterfall or the Beacon Badge. This is possibly due to the fact that gravity is not normal in this world; therefore, no extra effort is needed by the Pokémon to climb the waterfall. Also, given how the player appears to be "surfing" on the waterfall's surface, it may be that the waterfall isn't being "climbed" at all.
The distortion world doesn't really have a use at all. Its where Arceus banished Giratina because our innocent ghost was so called 'violent'. In platinum, the distortion world was revealed when Cyrus got in over his head and pissed off Giratina. Aside from story purposes, the only other use is to nag the griseous orb post game in platinum
Finally, there is no connection between Giratina and antimatter at all. When you think about how Dialga and Palkia represent time and space, it doesn't make sense at all, scientifically speaking. I asked about that here and gamefreak's excuse was that antimatter is more of an inspiration rather than scientific. If you're interested this is a theory about what Giratina would represent scientifically because if it truly was antimatter, it would just destroy the Pokemon universe because that's how antimatter works