The Document Object Model is an API for HTML and XML documents. It provides a structural representation of the document, enabling the developer to modify its content and visual presentation. Essentially, it connects web pages to scripts or programming languages.
All of the properties, methods, and events available to the web developer for manipulating and creating web pages are organized into objects (e.g., the document object that represents the document itself, the table object that represents a HTML table element, and so forth). Those objects are accessible via scripting languages in most recent web browsers.
The World Wide Web Consortium establishes a standard for the DOM, called the W3C DOM. It should, now that the most important browsers correctly implement it, enable powerful cross-browser applications.
Why is the DOM important?
"Dynamic HTML" (DHTML) is a term used by some vendors to describe the combination of HTML, style sheets and scripts that allows documents to be animated. The W3C DOM Working Group is working hard to make sure interoperable and language-neutral solutions are agreed upon (see also the W3C FAQ). As Mozilla claims the title of "Web Application Platform", support for the DOM is one of the most requested features, and a necessary one if Mozilla wants to be a viable alternative to the other browsers.