Graceful degradation is one solution for practice of building a web site or application, so it provides a good level of user experience in modern browsers. However, it will degrade gracefully for those using older browsers. The system may not be as pleasant or as pretty, but the basic functionality will work on older systems.
A simple example is the use of 24-bit alpha-transparent PNGs. Those images can be displayed on modern browsers without problems. IE5.5 and IE6 would show the image, but transparency effects would fail (it can be made to work if necessary). Older browsers that do not support PNG would show alt text or an empty space.
Developers adopting graceful degradation often specify their browser support level, e.g. level 1 browsers (best experience) and level 2 browsers (degraded experience).