Texture gives an image depth and presence. It is a very important aspect of how we perceive art and photography. Texture is not limited to soft, fuzzy, or coarse things like blankets and carpet. Things like glass bottles have texture too, they are just smooth, hard, and cold, possibly sharp or loads of other things as well. I find that smoother surfaces tend to get left out when talking about texture.
The image above is of the bottom of a vintage mirror frame hanging on a white wall. It is a solid, wooden frame, the actual surface is rather smooth but the frame gives the illusion of roughness. The withered look of the frame comes from the thick coat of matte white paint, layered haphazardly over the brown wood. In some areas the paint is flaking off the frame, creating imperfections and blemishes on the ornate carvings in the wood. The harsh way the paint is laid on the wood is scratched and gritty. The wood of the frame is carved into a chunky organic pattern. The terminal points of this pattern ending in blunt paisley like shapes. Shadows are created by the inset patterns on the paisley shapes. These inset pattern gives the frame depth, and a certain fluidity on its rigid surface.
The wall behind the mirror also has a slight texture. The wall is solid and bumpy. The white paint has a slightly glossy finish. The small bumps and lines on the wall are random and rigid. They cast the smallest of shadows back onto the wall. Due to the wall being repainted so many times the paint looks as if it has been caked on, it is obvious that the paint is heavily layered.