Texture to me is one of the most interesting features of composition. After all, a photograph is generally found on flat, smooth surfaces with no real textures to feel. But photographs can imply textures in a variety of ways. The roughness of tree bark, the smooth surface of still water, raindrops on flower petals, all these kinds of things affect the mood of an image through implying texture.
The photograph to your left is basically a picture of texture. I loved the way the rain drops weighed down the lower petals of this flower to separate them from the rest. This allowed me to shoot the textures of the raindrops and the textures of the edges of the petals above. On the other hand, the flower below contrasts the smoother textures of the flower with the rougher textures of the leaf below it.
You can combine contrasting textures using the rule of thirds. The photograph above is nearly split through the middle, but the photograph below puts the rougher textures in the lower third of the frame and the smoother texture with radial pattern in the top two thirds of the image.