The trails are due to the fact that the earth rotates. From our (or our cameras) point of view, the stars move in a circle around a point directly above the North or South pole (depending on what hemisphere you observe from).

The trails will differ depending on what latitude the person is at when taking them and in what direction the camera is facing. For example if you are at the equator and facing east the star trails would go vertical, at the poles it would be horizontal.