Happy to assist. There is a lot of information out there regarding how 120hz works, so this isn't a definitive definition or explanation by any stretch, but a simple "point in the right direction", and of course, feel free to follow up with questions. Minus a few internal "how Samsung does it" questions, general questions are welcome.
The panel is a 1920x1080 resolution that shows the picture at 120hz. There's no exception to this equation, as the panel IS a 1920x1080/120Hz panel. So any signal coming in must be upconverted to a 1080/120Hz picture. When smaller resolutions like 480 are upconverted (standard definition), the picture has to be expanded, which is why the lack of clarity is there. There's not enough information for the individual pixels, so the television has to compensate.
There is processing - like AutoMotion Plus - that will help improve the picture quality, but just like any rendering, there is only so much you can do. Think of zooming in too far on a small icon on your computer, and that's the general idea of what happens with SD pictures. While the expansion of the incoming picture happens regardless of the quality and resolution of the picture, the actual processing, which is additional, can be toggled off.
480i at 30Hz becomes 1080p at 120Hz.
720p at 60Hz becomes 1080p at 120Hz.
1080i at 60hz becomes 1080p at 120Hz.
and so forth....
When I say becomes, I mean it converts it to that, since that's what the panel will show. While it's not printed, it's "to be understood" that the upconversion is what happens.
AutoMotion Plus processing can be added to improve the picture of any of those equations to improve the picture quality, but that also can be turned off. The fact that the upconversion happens, however, is not something you can turn off.
You can't watch a 480i/60Hz signal on a 1080p/120Hz panel in 480i/60Hz. It just doesn't work that way. So it's understood - again - that the picture is upconverted to show on the resolution that is available.
Not to beat a dead horse, but there are some older 720p panels out there. You can't watch a 1080p picture on a 720p panel, so the opposite would happen in this case: The picture would downconvert to 720 and show that resolution on the panel, because that's what the panel is.
How does 60hz become 120Hz? By cycling the frames twice instead of once on the panel. Doubling the speed reduces the motion blur often associated with LCD panels. The benefit of 120Hz is that it divides evenly into the three major Hz signals - 24, 30 and 60Hz. This way, frame interpolation is avoided. Frame interpolation is a fancy way of saying that the TV doesn't have an actual frame to use, so it takes two frames, and sticks a "between A-and-B frame" inbetween to "fill in the gap". 30 and 60 divide into 60, but 24Hz has a 3:2 pulldown. With 120hz, 24 is divided evenly 5 times, and 30 and 60 divide evenly too. This provides a more realistic - and enjoyable - solution.
Does that help explain? If not, keep asking questions. That's what we're here for.