I studied the picture looking for evidence of motion artifacts that would occur if the arm/leg (I'll call it an arm to save keystrokes) moved into the frame with the shutter open. I don't see any. The arm has definite boundaries on both sides. One boundary is a little blurred, but even if the arm was moving across the frame while the shutter was open, wouldn't you see a blurred image of the arm all the way to the edge of the pic? The right hand edge of the sleeve is distinct. The light reflecting on the wrinkles is distinct too, and that would have smeared across the frame if the arm moved into the frame with the shutter open.
Another possibility is the arm was moving slowly relative to the shutter speed of the camera. This would minimize motion artifacts, but then the arm wouldn't be transparent in this case either. About the only way to make a real arm look like this would be to either double-expose (a bit hard to do with a webcam, though with some help from Photoshop it could be done after the fact), or the arm would have to "appear" in that spot, or "disappear" from that spot, without any visible motion, while the shutter was open.
What I'd really like to know is what the frame rate of the camera is. Being a webcam, it might be one frame per second or slower, but I can't be sure. I assume this "arm" appeared in only one frame, right?
Another interesting tidbit of information, that might be useful to someone who's more of a photo expert than me, is the exposure level across the 3 pics. If you look at the 1st pic's background (behind the arm), and compare it to the 3rd pic, the brightness is similar. The 2nd pic is brighter. I'm guessing that the "arm" partially blocked light from entering the camera, and it raised its exposure level momentarily, after the shutter closed while taking the arm pic. Thus the pic immediately afterward was overexposed, then the camera re-adjusted itself back to the level consistent with the light level in the room, resulting in the 3rd pic. Based on that, I wonder if the "arm" appeared in front of the camera during the exposure of the 1st pic, and remained during the interval between the 1st and 2nd pic, then disappeared right before the 2nd pic was snapped, causing the lighter exposure. By the time the 3rd pic was taken, the camera finished adjusting its exposure level.