Pokemon Diamond and Pearl is set in the Sinnoh Region of the Pokemon world. Pokemon are battle monsters that the trainer captures and then raises them leveling them up the more battles that are won. After a certian point the creature can evolve in a more advanced form, however evolution can be halted if desired by the trainer. The main premis of the game is to fill a pokedex, or a database, of all the pokemon available in the region. The easiest way of doing this is to travel around to the different cities of the region and battle different pokemon. At some of the cities there are pokemon gyms where the trainer can battle a gym leader in order to get a badge. This badge signifies that the trainer has mastered fighting that specific pokemon type and some areas can only be unlocked once a certian badge has been obtained. Once all badges are collected the trainer can then challege the Champion of the Pokemon League as a final gym.
The game does not just revolve around the pokemon gyms or trying to fill out a pokedex. The storyline of the game also has an antagonist called Team Galactic. As the trainer goes from city to city more of their plot in unraveled. Their goal is to create a pokemon utopia by unleashing the pokemon Palkia or Dialga. In order to find this pokemon they must lure it out by capturing a Mirage pokemon at one of 3 lakes in the region. Once the pokemon is captured then either Palkia or Dialga appears threatening to tear the world apart. After battling the pokemon the trainer can either capture or defeat it to cease its destructive force. After the game is beaten new areas unlock so you can fill up your pokedex completly.