The architecture design document is a technical document describing the components and specifications required to support the solution and ensure that the specific business and technical requirements of the design are satisfied.
An excellent example of an architecture design document is the Cloud Infrastructure Architecture Case Study White Paper article that can be found at http://www.vmware.com/files/pdf/techpaper/cloud-infrastructure-achitecture-case-study.pdf.
The architect creates the architecture design document to document the design factors and the specific choices that have been made to satisfy those factors. The document serves as a way for the architect to show their work when making design decisions. The architecture design document includes the conceptual, logical, and physical designs.