You must migrerate six Pokemon from a Game Pak to your game, which can be done by inserting the Game Pak into the area at the bottom of the DS Lite/Phat. Then, on the main game menu, select 'migrerate from -game name-', though the method in B/W is rather different. Once this has been done, see the man blocking the entrance, who will now let you inside to capture the migrated Pokemon. Only six Pokemon can be in the park at once - and you can't enter if the amount is any less than 6.
So, the reason he won't let you in is that you don't have to own a Pokemon from another Region - you must have migrated six.