Your collected stars open up the chat functionality for you. Once you've reached level five in your general progression, you can chat with other players. Your current progression level is displayed next to your avatar as a number in a circle.
To chat with another player, open an ongoing classic game, then tap the white speech bubble in the top right-hand corner of the screen showing your game. The bubble appears right next to your opponent's avatar. This will open a chat screen where you can type a message to the player.
Next, hit "OK" to start the conversation!
You won't be able to chat with players who have their chat turned off or who haven't reached level five yet.