A DTD is a formal description in XML Declaration Syntax of a particular type of document. It sets out what names are to be used for the different types of element, where they may occur, and how they all fit together. For example, if you want a document type to be able to describe
Lists which contain
Items, the relevant part of your DTD might contain something like this:
<!ELEMENT List (Item)+>
<!ELEMENT Item (#PCDATA)>
This defines a list as an element type containing one or more items (that's the plus sign); and it defines items as element types containing just plain text (Parsed Character Data or PCDATA). Validating parsers read the DTD before they read your document so that they can identify where every element type ought to come and how each relates to the other, so that applications which need to know this in advance (most editors, search engines, navigators, databases) can set themselves up correctly.
The example above lets you create lists like:
How the list appears in print or on the screen depends on your stylesheet: you do not normally put anything in the XML to control formatting like you had to do with HTML before stylesheets. This way you can change style easily without ever having to edit the document itself.
A DTD provides applications with advance notice of what names and structures can be used in a particular document type. Using a DTD when editing files means you can be certain that all documents which belong to a particular type will be constructed and named in a consistent and conformant manner. DTDs are less important for processing documents already known to be well-formed, but they are still needed if you want to take advantage of XML's special attribute types like the built-in ID/IDREF
There are thousands of DTDs already in existence in all kinds of areas (see the SGML/XML Web pages for pointers). Many of them can be downloaded and used freely; or you can write your own (see the question on creating your own DTD. Existing SGML DTDs need to be converted to XML for use with XML systems: read the question on converting SGML DTDs to XML, and expect to see announcements of popular DTDs
becoming available in XML format.