When I think of a design brief I think it should have:
- The overall target audience the design is to be aimed at
Many factors can come into play when deciding an audience. Some people will argue that certain typography and colors could be associated with a particular audience, as just one example.
- Where is the design to be delivered
You should know if you need to communicate with someone else like a print shop or advertising agency that is going to use your design.
- Finished file type
Whether the client is going to expect source files, a template to be repurposed or a PDF.
- Set Budget for the project
Not just for the design but factor in any additional time that may be needed for bringing any source files up to spec for the design project
- Schedule time expectation
This is a very big one that I think gets over looked and I've seen some designers get burned. If you are going to provide multiple iterations or if the process is phased than each phase should detail the time for completion; and the expected time the client is to have it approved, typically 24-48 hours. If you don't set times and you come up on the deadline, the client can and will expect you to finish within 24 hours and blame you if you don't have it in writing.
- Source files from who and time deliverable
Some projects a client will rely on another person brought into the mix and if you have a tight deadline and the client's photographer or illustrator didn't meet the time they were supposed to provide the material for you to do the design that will fall on you to still meet the deadline.
- What is the client's goal for the project
Knowing the goal in the brief will help the creative process
- Revision expectation
Not every client will like your design off the bat so in the brief it needs to be determined if there are a set of revisions that may be expected since you're here to not only provide a service but you need to make money.
- How many versions are to be submitted
We all have a standard norm to our design process but the brief in regards to versions provided some clients may expect a logo design to have on the first submission four or five.
- What is the business background and mission statement
The business background could be a key factor in the design, also help in the target audience and overall creative process in the design.
Do they have examples or ideas in mind
Sometimes you're fortunate to have an expectation or examples of how the client wants their design project to be because a client that has no clue is dangerous and you could be jumping through hoops trying to figure out what they want when in the end of a terrible project they never knew what they wanted in the first place.
A couple good articles on the subject that come to mind are How To Write An Effective Design Brief and Get The Design You Want! and The Ultimate Design Brief.