Graceful degradation
Graceful degradation is the ability of a computer, machine, electronic
system or network to maintain limited functionality even when a large
portion of it has been destroyed or rendered inoperative. The purpose
of graceful degradation is to prevent catastrophic failure.
Graceful degradation is one solution. It is the 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 PNG images. Those images can be displayed on modern browsers without problems. Internet Explorer 5.5 and Internet Explorer 6 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).
Progressive enhancement
Progressive enhancement is a strategy for web design that emphasizes
accessibility, semantic HTML markup, and external stylesheet and
scripting technologies. Progressive enhancement uses web technologies
in a layered fashion that allows everyone to access the basic content
and functionality of a web page, using any browser or Internet
connection, while also providing an enhanced version of the page to
those with more advanced browser software or greater bandwidth.
Progressive enhancement is similar concept to graceful degradation but in reverse. The web site or application would establish a base-level of user experience for most browsers. More advanced functionality would then be added when a browser supports it.
Progressive enhancement does not require us to select supported browsers or revert to table-based layouts. We choose a level of technology; i.e. the browser must support HTML 4.01 and standard page request/responses.
Going back to our image example, we might decide that our application should be functional in all graphical browsers. We could use a lower-quality GIF images by default but replace them with 24-bit PNGs when the browser supports them.
Links
Wikipedia: Progressive enhancement and Graceful degradation (fault tolerance)
Source: SitePoint Blog