On my car, a golf rabbit 2007, there is a lining on both sides near the bottom of the frame. Its surface is rougher than the rest of the body panel surfaces Anyone have an idea what this part is called?
As @Paulster2 has stated the part of the body below the doors is referred to as the rocker panel. It is typically steel but may have decorative plastic trim covering it. Due to its' close proximity to the ground it may have a chip resistant coating. This coating can have a rough "pebbled" texture and can be the same color as the body or a contrasting color.
If it's the part just below the door, it's called a rocker panel.
Depending on the country it is also known as the sill...