A Listener window is like an advanced chatbox. It's designed to help you manage messages easier when there is a lot going on. It can help out even when there isn't much going on either, relieving you of the stress that is trying to keep track of what is going on, especially when you're busy with something else at the same time.
Listener windows are unique in that they can filter out what shows up in the chatbox. For example, to hide a certain player from showing up, just hold shift and right-click them. You can see who's hidden by clicking the "eye" button in the top right corner. Clicking the X will hide the window, and you can get it back by clicking the minimap button.
To add a player back, you can either shift-right-click their faded text when "show hidden" mode is on, or target them and then click their name in the top left corner. Another way to easily add people is using the key binding available (see the Key Bindings options).
The window can be configured by right clicking the top left corner. There you'll see some options:
This is an option that inverts the player filter. When this is off, the Listener chatbox will only show people that you have specifically added. When it's on, it will show everyone unless they have been specifically removed. Ideally, you want this "on" when in a less crowded area, and then "off" when trying to manage something in a more crowded area, where a lot of the chatter going on is irrelevant to yourself. A shortcut to toggle this feature is to just shift-click the menu button.
With this selected, Listener will play a beep when the window prints a new message. You can also configure it to flash the taskbar icon. For example, with this on, you can tab out, and then when you see the taskbar icon flash, you know that someone has emoted around you in the game, and you can take care of it.
With this enabled, the window will open up automatically when it receives a new message (which isn't filtered out), so you can close it whenever by clicking the X, and then it will open when you get a message on the channels and/or players its listening to. This feature may be useful for channels you may be in that don't get much activity, so you can close the window and forget about it until someone talks in them.
This option locks the frame from being dragged. Normally you can move the window around by dragging the titlebar. Even when this option is selected, you can still hold shift to move the window.
This button opens up a window that contains the text of the chatbox, so you can copy it.
This menu allows you to select which chat events should show in the chatbox. "Public" is /say, /e, and things like /wave. You're probably familiar with these sorts of filters with the regular chatbox settings.
Players (Group only)
When in a group, this option will show, and it will allow you to add or remove players in your group to the filter. For example use of this, if you wanted for some reason to listen to the players Leeroy and Jenkins, first you turn off "Inclusion" mode, and then open this menu. There you can select Leeroy and Jenkins to be added to the chatbox.
Raid Groups (Raid only)
When in a raid, this option will show, and it will allow you to add or remove whole raid groups to the filter. For example, you might be running a scenario where group 3 and 4 are following a different trail, and you can create a new window to show those two groups only to better manage things.
Whoever shows up in the chatbox is controlled by a simple three states. First is the inclusion mode. If off, then they default to off. If on, then they default to on. Then is the group tri-state. If they're part of a group that's set to ON, then they will be switched on, and off will switch them off. Neutral won't override their default value. Finally on top of that there's the player-specific filter, which trumps the previous two states.
Default/Inclusion -> Group Filter -> Player Filter
This button opens up the frame settings for per-frame configuration. Additional settings can be found by right-clicking the minimap button.
As of 2.0.0, Listener can create multiple windows, each with their own configuration, filters, and events.