Cleanness is essential for a good web design. Many people mistake clean design for minimal design. Both styles have things in common, but they are not the same. While minimal design is about using the bare essential elements in designing a website and doing more with less, clean design is more about having every element exactly where it needs to be.
You can have a site full of unnecessary elements, but still keep each one of them in its place. Clean web design is an effective way to convey an image of elegance.