LG are the first to bring a smartphone with the powerful Snapdragon S4 Pro chipset and they've enabled several features on the Optimus G that both showcase that power and improve multitasking.
You can watch LG's official demo video to see them in action:
The Q Slide feature lets you use two apps at a time, at least in some scenarios. One app becomes transparent (you can adjust opacity with a slider) so you can switch to another app without completely losing sight of the first one.
There are a couple of more video-related features that leverage the S4 Pro chipset. Dual Screen Dual Play lets you do wireless TV-Out with the Optimus G, but unlike the TV-Out features on most other phones, this isn't simple mirroring but screen extension instead.
That means the two screens can show different things, e.g. a video on the TV and an app on the device. The phone is pretty smart and figures out what goes on which screen. You can also do presentations while reading your notes, plus there's a virtual laser pointer function included.
Yet another video feature lets you zoom in on a video, while the video is playing. You can zoom in up to 5x if you really want to go to that much detail.
Then there's Quick memo, which we've seen on the LG Optimus Vu. To trigger it on the G, you press both keys of the volume rocker and then you can scribble on a note. If you tap the overlay button, that note will remain visible on the screen even as you navigate to something else.