Texture comes from textura "web, texture, structure," from stem of textere "to weave," hence textile. Every single, solitary surface has texture. Smooth as in glass, marble, mirrors, chrome, satin, etc. or rough as in bark, cement, stucco, burlap, etc. Texture is the surface quality of an object.
In the above photo, the white melamine surface is smooth, shiny and hard while the fabrics are smooth, matte and soft. The fabrics themselves look like textured items but they are two dimensional. These give the illusion of touch. They are examples of visual texture, created with the material that we use.
The photo below is very tactile. The objects are soft, hard, shiny, dull, flat, rounded, and very touchable because they are three dimensional. Physical texture is the texture that you can actually feel with your hand.
Texture is what gives a design the feeling of surface. It is the tactile sense of the elements in the design. It is a supporting player in design. If you have good colours in appropriate values in a project but something isn't just right, try changing the visual texture. This is best understood by comparing an unquilted top with a finished quilt. What happens is that a variation is introduced that varies the pattern of light and dark areas on an object.
It may help to understand texture by looking at food. Compare smooth cream of wheat with crunchy granola. Soothing macaroni and cheese as opposed to tantalizing Thai style stir-fry. Different textures for different occasions. Can you feel the difference?