The Red Orb and The Blue Orb are items which are bound to specific legendary Pokémon.
They are use to control Groudon and Kyogre.
In Gaining Groudon and The Scuffle of Legends, it was revealed that Maxie had the Blue Orb and planned to use it to control Groudon, while Archie had the Red Orb and succeeded in using it to control Kyogre.
Maxie lost the Blue Orb when Pikachu became possessed by it after grabbing the orb off of Maxie's desk. It was shown that the both orbs can be absorbed into the body of and possess any person or Pokémon that touches them. This can happen instantly, as was the case with Pikachu, or over time, as was the case with Archie.
A human or Pokémon being possessed by one of the orbs will have the corresponding legendary Pokémon's special red or blue markings appear on their body. While possessed, Archie was still able to control Kyogre, but Pikachu went on a wild rampage. When Kyogre was hit by Groudon's SolarBeam, the Red Orb extracted itself from Archie's body and he lost consciousness briefly. The Blue Orb also extracted itself from Pikachu. When he woke up, Archie seemed to have no memory of what happened while he was possessed. Both orbs shortly dissipated into the sky and have not been seen in the anime since.
It is assumed that they were both destroyed so that evil people could never use them again.