Pokémon Platinum is the 3rd edition of the 4th Generation main series games. While it is not a sequel to Pokémon Diamond & Pearl, it is actually an extended version of the previous main series games. In Pokémon Platinum, a lot of things have been changed and updated. However, the storyline still takes place in the region of Sinnoh. The main Pokémon in this game is Giratina instead of Dialga & Palkia, Giratina also appears on the box-art of the game. Instead of capturing Dialga and Palkia at Spear Pillar, Giratina will the Pokémon you have to capture and save from Team Galactic.
In Pokémon Platinum, they introduce many new characters, such as a new detective codenamed "Looker" who appears in the game throughout the storyline trying to track Team Galactic. In addition to new characters, in Pokémon Platinum, the region of Sinnoh now takes place in a more colder weather making the main characters appear in clothing more appropriate for the weather. You also encounter many characters more frequently in many different new locations.
While Pokémon Platinum still uses the same game engine as Pokémon Diamond and Pearl, it has had an improvement in the graphics department while also having a lot more 3D elements. Giratina appears in a new Origin form which can only be seen in the Distortion World or if you use the Platinum Orb. Skaymin also appears in a new Sky form which is a completely different design than the normal Shaymin form. This Sky form gives Shaymin new stats and the opportunity to learn new moves. It can only change forms if you use the special Gracidea Flower on it, but only under certain occasions.
One of the new area’s in Pokémon Platinum is the Distortion World, which is where Giratina resides. The Distortion World has many more 3D elements than anywhere else in Sinnoh, you even have the ability to walk on ceilings etc.
There are many more features in Pokémon Platinum, so much that they need their respective pages in order to be fully detailed. Look on the right and you will see links that take you to various guides explaining all the features in the game.