Parallax: As the viewpoint of the player moves side to side, the objects in the distance appear to move slower than the objects close to the camera. Para X and Para Y define how fast the background layer moves (x-axis and y-axis).
clipping: means that only visible objects will be calculated. If the teeworlds sun in the background moves out of the visible range, the pc still calculates where it is supposed to be rendered. If you use clipping you define an area within the sun will be rendered.
shift usually means that you can change the value more exact as the values change more slowly.
Antoine de Saint Exupéry: It seems that perfection is reached not when there is nothing left to add, but when there is nothing left to take away.
Besides - I am the gfx guy!