Definition

A design document is a technical report that outlines the implementation strategy of a system in the context of trade-offs and constraints.

Goal

Think of a design document like a proof in mathematics. The goal of a proof is to convince the reader that the theorem is true. The goal of a design document is to convince the reader the design is optimal given the situation.

The most important person to convince is the author. The act of writing a design document helps to add rigor to what are otherwise vague intuitions. Writing reveals how sloppy your thinking was (and later, code will show how sloppy your writing was).