DOM is an abbreviation for Document Object Model, a platform and language neutral interface that allows programs and scripts to dynamically access and update the content and structure of documents.
The Document Object Model provides a standard set of objects for representing HTML and XML documents, a standard model of how these objects can be combined, and a standard interface for accessing and manipulating them. Vendors can support the DOM as an interface to their proprietary data structures and APIs, and content authors can write to the standard DOM interfaces rather than product-specific APIs, thus increasing interoperability on the Web.
The goal of the DOM specification is to define a programmatic interface for XML and HTML. Since various levels of the DOM are differently separated (Level 1 has core and html parts while Level 2 has core, view, events, style, etc. parts, as well as Level 3 has different parts again), this post provides the link to W3C index of all these specifications.