Pal Park is a location at the east of Route 221 where you can migrate your Pokémon from the previous versions of the GBA games (Ruby/Sapphire/Emerald/FireRed/LeafGreen). It can only be accessed after you have defeated the Elite Four.
When you first visit Pal Park, you will meet Prof. Oak, and he will gives you a National Pokédex. He lives in Eterna City.
In order to migrate your Pokémon, go to the title screen (where there are the Continue and New Game button) and select "Migrate Pokémon" with a Pokémon catridges of the earlier versions (Ruby/Sapphire/Emerald/FireRed/LeafGreen) inserted in your Nintendo DS. The Pokémon shown in there is the Pokémon you store in the PCs of the GBA catridges. Migrate them to here and the Pokémon in the GBA catridges will be gone. Only 6 Pokemon at a time. After migrating the 6th Pokémon, you need to wait another 24 hours if you want to migrate again with the same game pak. Changing the time on your DS will delay another 24 hours of migrating.
Next, the migrated Pokémon will be found in Pal Park. Head to Pal Park and the person will give you some special Poké Balls, depending on how much Pokémon you migrated. Then head to the grassy area or water to find them. The special Poké Balls have a 100% catch rate. The time taken for you to catch those Pokémon is also recorded.
Pal Park is also found in Pokémon SoulSilver and HeartGold. It is found in Fuchsia City in Kanto, where Safari Zone used to be. Pal Park looks and works the same way as in Diamond and Pearl, but the 24 hours migrating limit has been removed.
Pal Park may also be used to get all the starter Pokémon from GBA games, since you don't have to beat Elite Four in those games to migrate Pokémon to newer games. You just have to capture 6 other Pokémon, making you have 7 Pokémons. You then just put 6 of them into your PC, and you can now migrate to newer games. Then you would just start a new save and do it again with another starter Pokémon.