Have you ever been making a turn in traffic, and thought that all of the cars ahead of you seemed to have the turn indicators in sync? After watching for a moment, you realize some are slipping out of sync, and they begin to look random or chaotic again. If you wait long enough, they'll seem to be in sync once again...
This is related to the concept of a moiré pattern, where regular intervals of one thing seem to alternately line up and then fail to line up with the regular intervals of another thing. The Wikipedia page linked shows some good examples, such as this:
An emergent property (a third pattern) is visible, but in reality there are only two sets of parallel lines at an angle to each other. The combined pattern has alternating areas of white and dark space, because of the particular amount of overlap varies with position on the intersecting lines.
If you take video of someone with a finely striped or plaid shirt, you may notice a similar effect.
What is happening is the pixels of the CCD in the camera are lining up with the subject material unevenly. Sometimes the pixels line up well with light areas of the subject, and other times they "miss" or see dark areas of the subject. The result can create a new, unwanted pattern.
When you take video of an LCD screen, the same thing is happening, but the pixels of the display are alternately lining up and "missing" the sensors in the video camera.
The curved shape happens due to another effect, parallax. If the plane of the CCD is exactly parallel to the plane of the display, the curved shapes should not appear. But if the planes are not exactly parallel, you introduce different frequencies of the regular pattern of pixels (either display or CCD). As that frequency changes, the moire pattern changes its appearance, which results in the curved lines.
There's even more to consider, and that's the frame rate of the video device and the refresh rate of the display, which can add flickering and apparent bright/dark lines that seem to move during the video. It's the same concept, but with a time dimension.