The Holiday Worlds of Old are separate realms that are each linked together and the real world.
The seven Holiday Worlds represent Independence Day, Halloween, Christmas, Thanksgiving, Easter, St. Patrick's Day and Valentine's Day. Each Holiday World provide whichever holiday it is associated with to the real world, which are celebrated and cherished by humans all over the world. These worlds are said to be where Holidays originated from.
The Holiday Worlds are accessible through Holiday Doors, as seen in the Hinterlands outside of Halloween Town. The only worlds shown in the film are Halloween and Christmas.
In the epilogue of the film, it is revealed that none of the inhabitants of each Holiday World knew of each other's existence until after the Christmas calamity that Santa Claus fixes.