Your Dorm Tower is a special place where you rent out rooms to Dormmates to increase your Strength and Intelligence stats.
You can access your Dorm Tower by tapping the "Dorm" button in the top left corner of your main profile page. Or by tapping the menu button on the top right and then tapping "Dorm Tower".
Once there you will have an overview of your Dorm Tower. From this screen you can spend Cash to build new Floors and Rooms to rent to new Dormmates.