Taking a good photograph of a shiny metal object can be problematic because of light reflections creating highlights off the surface. Here's a picture of the back of a pocket watch used by John Wesley Powell during his trailblazing boat trips through the Grand Canyon (1869-1872); the shiny gold surface results in major problems with highlights (click on the photos for a full-scale view).

By fitting a light curve to every pixel, RTI essentially "smooths out" high points in the light curve, eliminating reflected highlights. Here's an RTI image, slightly modified using Photoshop to enhance contrast:

This is with the virtual lighting direction directly overhead; in the RTIViewer software, you can dynamically change the virtual lighting direction to anything you want, revealing additional details.