Interface design is the arrangement and makeup of how a user can interact with a site. The word interface means a point or surface where two things touch. So a web user interface is where a person and a website touch - so menus, components, forms, and all the other ways you can interact with a website.
Good interface design is about making the experience of using a website easy, effective and intuitive. It's actually much easier to demonstrate bad interface design because that's when you really notice it. A simple example of interface design is the use of icons. Have you ever looked at an icon and thought "what is that meant to represent?!" - well that would be bad interface design. Using icons to label and signify different types of content or actions is just one part of interface design.