The phone was added in the 1.2.0 update. Prior to this update, a button used to access Daily Challenges was in the place where the CPI Phone button is currently located.
In 1.8.0, Island Live was added to the phone. It contains various features:
Events: Shows ongoing events, such as recent additions to the island, or parties. It also displays the duration they occur, and a "go there" button to transport the player to the area the event occurs.
Daily Challenges: Displays Daily Challenges. If a player completes all five challenges for the day, they can also receive a bonus of 50 coins, although this bonus is only possible with membership.
Adventures: If the player is on an adventure, it will display the name of the adventure and the next task the player must complete. If this is active, the daily challenges section will not appear. If the player is not on an adventure but has an uncompleted adventure, it will display an uncompleted adventure, and the rewards received from it. If this is the case, the daily challenges section still appears.
Live events: Displays a countdown that shows the time until the next time a mini-game occurs, such as Tilt-o-Tube, the Crate Co. target game, and Team Dance Battle, and also provides a "go there" button.
Level rewards: Displays the experience bar of whatever level rank is closest to reaching the next level, and suggests methods to gain XP corresponding to that rank. It also shows which level pack will be received next, and a few sample rewards from the pack. This will not appear if the player is at max level.
The top left corner of the phone's menu displays a reception bar. However, it has no relation to the player's internet connection, and is purely aesthetic.