It's not a building you put in your city, it's a weekly tournament you've gained access to. When you win battles where your highest aged unit is of the age of the province with the tower, you gain points in that tournament, at the end of the week if you had enough points to hold a high enough rank you get medals. Medals are used to buy expansions for your city, buy extra attempts in guild expedition and siege guild vs guild sectors in the all ages area.