The Digger in Pokémon Brilliant Diamond and Brilliant Pearl gives you access to the Secret Bases, a way to set up a small area in the Great Dungeon where you can place specific statues. The Digger Drill is an object that you will have to unlock by working on particular tasks in the game. Here's where you can find the Digger in Pokémon Brilliant Diamond and Brilliant Pearl.
You will need to talk to the old man who gave you the Explorer Kit in the first place, the one from Evisopolis near the Pokémon Center. Talk to him about the tasks he wants you to do and everything he assigns you to do. Eventually, he'll give you the task of digging for fossils in the walls of the Grand Underground. When you return to him after completing this task, he will reward you with the Digger Drill.
The next task he gives you is to use the item on one of the walls to create a secret base, which is the whole reason for having the Digger Drill. You can use the item by having your character face a wall and interact with it. When you do, you'll create a secret base where you can place any of the statues you've found while digging for fossils in the Grand Underground.