Mirror mode is when whatever is on your laptop screen is "mirrored" to your external (HDTV) display. So, on both displays, you see the exact same thing, at the same resolution. Probably not what you want.
When you have your displays set to "extend" (which is the other method you described), it means that one of your displays is the primary screen, and the other is the secondary screen. From what you described, the laptop screen was the primary (with the normal desktop screen w/all icons), while the HDTV was the secondary (just the wallpaper and sometimes the mouse pointer). You probably have it set to where the extended screen is on the right of the primary. What that means is that if you move the mouse to the far right of the laptop screen, instead of just ending there, it will "extend" over to the secondary (HDTV) screen. So, as described in the previous posts, if you were to grab a safari window and drag it to the right, you could actually drag it to display on the HDTV. Everything is assuming your settings are set to extend to the right. Wherever your settings are set to drag, that is the direction where you can see the mouse, when dragged.
The way to change this, is in your System Preferences/Displays, make the HDTV the primary display, resulting in the laptop screen as the secondary. Now, the main desktop w/all icons should be on the HDTV at native resolution (assuming that to be 1920x1080). That is probably what you wanted in the first place. Then the laptop screen will be the extra desktop with nothing on it. Problem is solved.
When I have the HDTV set as primary, I then just lower the laptop screen brightness down to zero. If you also have it connected to a wireless keyboard/mouse, then you can just move the laptop to the side and use the keyboard/mouse and HDTV.
