The Earth Plate is one of several items in Pokemon Brilliant Diamond and Shining Pearl that boost the power of certain moves.
Ground-type moves will see a massive benefit from the Earth Plate. It is a held item that can be given to any Pokemon, but those of the Ground-type and with Ground-type moves will do the most damage.
If you are looking for this held item in Pokemon Brilliant Diamond and Shining Pearl, you'll find it in the Oreburgh Gate. This is a cave right next to Oreburgh City in Sinnoh.
Where to find the Earth Plate in Pokemon Brilliant Diamond and Shining Pearl
Pokemon Brilliant Diamond and Shining Pearl trainers will need to defeat a few Gyms. This is because three Poketch Hidden Machines must be usable outside of battle, in order to access the Earth Plate.
Those Gyms are Oreburgh City, Pastoria City, and Canalave City. These open up the ability to use Rock Smash, Surf, and Strength, respectively. Once they have been beaten, you can grab the Earth Plate.
Go to the city of the first Gym mentioned. In Oreburgh City, take the north path. There are a set of stairs you will reach that head down to a small cave. This is the Oreburgh Gate.
Move south after entering the cave and you will come to a body of water. Use Surf in your Poketch to head east across the body of water. A trainer will be by the staircase, which you'll need to defeat in battle.
After you beat the trainer, go down the stairs and use Strength to move the boulder. There will be two Poke Ball pickup items in this area of Pokemon Brilliant Diamond and Shining Pearl.
The one sitting to the south is the Earth Plate that you are looking for. Press A when you are near it to pick it up and add it to your Bag. Then give it to a Ground-type that you want to do some devastating damage.