Progressive enhancement is a method of developing web pages where you first make them work and look decent in base-level browsers and devices, and then layer on non-essential, more advanced CSS and JavaScript enhancements for current and future browsers with better support. For example, you may build a form in plain, semantic HTML that looks fine without CSS available and works without JavaScript enabled, and then enhance its appearance with CSS and its usability with JavaScript client-side validation, adding to server-side validation you already have in place. The goal is to create the richest experience possible for everyone by taking advantage of the capabilities of modern browsers while still making sites that are completely usable for everyone. The book Designing with Progressive Enhancement (www.filamentgroup.com/dwpe) sums it up nicely:
Progressive enhancement...aims to deliver the best possible experience to the widest possible audience—whether your users are viewing your sites on an iPhone, a high-end desktop system, a Kindle, or hearing them on a screen-reader, their experience should be as fully featured and functional as possible.