Alliances are a feature within the application that allow you to gain help from someone else in order to increase your chances of success during any battle. Your Alliances are essentially like a friends list. From this list of Alliances, you can pick which of their Set Guests you would like the help of.
Please note that you do not have control over this Guest, they will be an AI assisting you.
The Alliances page can be accessed through the application's menu button. From here you can check your list of alliances, sent & received requests, and ID search.