This should be developed by the client and the designer together in an ideal setting. The brief is very important as it forms the definition of the project. A typical brief involves an overview of the project requirements along with its aims and objectives. There should be a list of who is involved (stakeholders) along with its aims and objectives. It should also contain the expected deliverables, including some scheduling information and any milestones.
It's important to know who the audiences are; this is crucial as designs are done for the audience. The more you understand your audience, the better. The message should clearly be indicated, defining the purpose of the project and including other pertinent information. The more details, the more successful the design. The budget might be included in the brief, which allows me to know what I'm working with to avoid surprises.