Popular when Windows 3.1 was still the primary flavor of Windows, the multiple document interface (or MDI) refers to an application that can have more than one document open at once. This interface supported the philosophy of files of a certain type belonging to only one program -- .doc for Microsoft Word, .bmp for Paintbrush, .123 for Lotus 1-2-3, et cetera.
The multiple document interface has been abandoned by Microsoft in favor of the single document interface (or SDI), in which each instance of a program edits one document at a time. This better fits their philosophy of a document-centric interface, where various applications are merely tools to work on documents. Microsoft Word is an example of a program that has switched from a multiple to a single document interface.
Still, some programs have retained the MDI. Programs that use large amounts of resources, such as Adobe Photoshop, often have an MDI due to the prohibitive cost of running more than one instance at a time. Often, though, the MDI is retained simply due to tradition; programmers (and users) do not want to make the switch to a new interface design. The SDI is conceptually easier for novices to grasp, easier on the eye, and more straightforward to implement. Due to these benefits, the SDI is being used more and more often, and it may not be long before MDI fades forever into the mists of computing obscurity.
Thanks to StrawberryFrog for some helpful input!