When you enter the tower, you will be stopped by security who will explain that trainers come from far away in order to visit here. He will say that they run security checks to make sure that the younger trainers are safe and will then allow you to move on. The Tower is a 130 floor tower which will allow you to enter any floor.
When you make a trade with someone from a different region through the GTS or over WiFi, the region will appear on the list. As there are 130 locations, they take up each floor. The game will keep track of how many people you have traded with and will let you interact with these characters. The characters remember what you traded, when you traded and how many people the person itself has traded with. They tend to make a comment about the region and the various Pokémon they have traded