One of the key features of an advanced theme is a Theme Options page. A Theme Options page allows the theme user to supply information to the theme without having to modify the theme files. Although a single-use theme could have this information hard-coded into the theme, it's an inelegant solution. If the theme is used more than once or is managed by a non-developer, having an easy-to-change setting on the back end allows changes to be made quickly and easily.
Advanced uses of a Theme Options page vary widely and include design editors, color pickers, font options, and settings to modify the theme layout (switch a sidebar from one side of the theme to another, for example). The options offered depend on the project and the design. Early in the design process, consider what a user may want to modify.
Before jumping ...