The console is the text field that allows you to chat with other players or enter Commands. Among players, it is more commonly just referred to as "the chat."
How to Use
You can bring up the console by tapping the speech bubble icon in the bottom left of the screen. If you're on a desktop, you can press the t key as well.
Press enter to send the chat text (or command), and press the close keyboard button (iOS) or escape key (desktop) to cancel.
On desktops, typing the backslash automatically opens the console, enabling you to more easily input commands. You can also use the up arrow in an open console window to automatically retrieve the last thing you said or typed. Repeated use will take you farther and farther back.