When you enter the tower, you will be stopped by security who will explain that trainers come from far away in order to battle here. He will say that they run security checks to make sure that the younger trainers are safe and will then allow you to battle on. The Tower is a 130 floor tower which will allow you to enter any floor in order to battle trainers.
When you make a trade with someone from a different region through the GTS, 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