A design document is a detailed description of a software product that a software designer writes in order to give a large software development team a solid reference on what they're doing. A design document is practically required to coordinate a large team under a single vision.
A design document needs to be stable reference, and outline all parts of the software and how they will work. The document should give a fairly complete description while maintaining a high-level view of the software.
For game design, the document will often be between 50-200 pages.