The Phone icon can be found at the lower left corner of the main screen, and is an important tool for increasing intimacy with the four male characters.
It is used to store and send SMS, Moments, as well as your Phone Calls. (They can be replayed at any time. If you miss a call, don't worry, it'll be right there.) You can also read a few of the headlines of Loveland City In the News Section of your phone.
To check your intimacy levels, tap on the "Intimacy" button in the top right corner of the Messages and Calls sections. You will receive more opportunities to interact with your favorite male character as you go along in the game.