Pokémon Brilliant Diamond and Pearl are remakes of the original Pokémon Diamond and Pearl and retain many of the same features. One such feature that is carried over into the remakes is the VS Seeker. This item allows you to rebattle previously defeated trainers.
To get the VS Seeker in Pokémon Brilliant Diamond and Shining Pearl you will have to have beaten Team Galactic in Eterna City as well as receive the bicycle. Go south through Cycling Road and you will enter Route 207. Here, the Professor's assistant will give you the VS Seeker.
This handy item lets you challenge trainers you have already defeated. This is a good way to grind experience and money in Pokémon Brilliant Diamond and Shining Pearl. When you use the item, all trainers on the screen that can be rechallenged will have two red exclamation points appear over them.
When battling these trainers again, their Pokémon will become stronger. After using the VS Seeker, you will have to walk 100 steps before it is recharged and you can use it again. Lastly, it cannot be used inside buildings or caves.
For more information on Pokémon, check out How to get more honey in Pokémon Brilliant Diamond and Shining Pearl and How to get Munchlax and Snorlax in Pokémon Brilliant Diamond and Shining Pearl on Pro Game Guides.