Interface Design is a combination of many concepts that form the practice as a whole. Typically defined by Information Architecture, Information Design, Usability Testing and Graphic User Interface (GUI) Design. Interface Design is applied to areas that are necessary to organization and usefulness like navigation, glossaries, site layout, etc. How the user interfaces with the product allows the user to readily access what they are looking for quicker. Typically if an interface is frustrating the user will abandon whatever they are using. So the practice of making things easier and giving users information in a common pattern allows them to connect with your brand.
Some of the best examples of great interface design are ones that go by unnoticed on a day to day basis. We have become so accustomed to them that the interface has become expected. For instance, many products and websites use navigation structures that are on the left hand side and are in a column that is 10-30% of the page width. From Wikipedia to Facebook to WordPress to Gmail. These companies understand that consumers are used to using and navigating products this way. So instead of retraining a user and having long adaptation times they have taken a tried and true formula and applied it to their product so the user can interact with it the first time they see it.
Interface Design has begun tackling new problems with the rise of tablets and smart phones. The same patterns that typically work are no longer working on these devices because the lay of the land is so different. Many of these devices are touch screen sensitive which changes the way the user interacts with the product. Instead of a mouse pointer you have a finger. Fingers come in many different sizes and widths and are bigger then a mouse pointer. Taking that into consideration the way navigation and buttons are laid out on a page must be adjusted. Buttons should be bigger while content should be legible and minimized to the bare bones of what someone would need on a mobile device.