How a web page "degrades" refers to how it will be displayed by older or less popular browsers.
The hope is that the web page will "degrade gracefully," meaning the images and text will be displayed in roughly the same way across a variety of browsers and platforms. If a designer relies heavily on JavaScript, for example, then the site will not work correctly on older browsers and thus not degrade gracefully. This problem of browsers interpreting web pages differently is one reason why protocol is so important. If everyone agreed on one protocol for using HTML, then it would be considerably easier to control how web pages degrade.
