In Global chat you will be chatting with everyone from around the world.

In Alliance chat you will be chatting only with the members of your current alliance.

Chat also allows you to mute other players. You do this by tapping on a player and selecting Mute. Muting a player will remove them from your chat completely.

You can view players that you have muted by tapping the icon in the bottom right of the screen. From that screen you can unmute players.