Originally, Arceus was a being far more powerful than he is today. With his power, he created other Pokemon to create the universe. He created Palkia and Dialga to form time and space. He created Groudon and Kyogre to form land and sea. He created Mew, to populate the planet with other Pokemon. He created Kyurem-BW to create virtue, though, Kyurem later split into three forms. Many more dragons were created, including Giratina and Rayquaza each with their own purpose.
Arceus, through this process became spent, and fragments of his power broke away from him in the form of the plates. His multitype ability comes from him regaining some of his old power, if only temporarily.
When Groudon was formed, the Earth Plate fell. As Kyogre was created, the Splash Plate fell. As he created Palkia*, off came the Draco Plate. As he created Dialga, away came the Iron Plate. Whilst Giratina begun to breath, away came the Spooky Plate. As Rayquaza came into being, the Sky Plate fell. When Mew** was created, the Mind Plate fell. When Arceus created Kyurem-BW, he imbued upon it far greater power than any other, power perhaps to surpass his own and as such, 3 plates fell from Arceus that day - Flame, Zap and Icicle - which eventually divided into their respective dragons.
As the plates were found in Sinnoh, only records of Palkia and Dialga were found - Giratina being shunned for it's banishment. The engravings upon the plates show that the plates fell when Palkia and Dialga were formed, and so it makes sense that the other legendaries, formed by Arceus, gave their own plates.
To this day, it leaves some legends yet to be found. Xerneas accounts for the Fairy Plate, and Yveltal gives purpose to the Dread Plate*** - having been brought into life to guard Life and Destruction/Death.
This means, soon to come to life, are those representing the Fist, Insect, Meadow, Stone and Toxic Plates. These are the typings for the next 5 cover legendaries.
As for the 6th? Perhaps a new type shall be discovered, or Pokemon not of the original one shall come to be. Kyogre, Groudon and Rayquaza have no direct links to Arceus, so we may one day discover that they are not of His creation, but rather of Mew's.
*Kyogre is pure water, so Palkia cannot have the Splash plate. **Mew is the only non-uber to count. ***Palkia is Draco, meaning Rayquaza is Sky and only leaving Dread for Yveltal.
And if anyone takes this seriously, you're a moron.