Provide the context for the design project. What market is your company or product operating in, how is it positioned in relation to competitors and how is it performing? What issues does it face?
It may be helpful to define your project in terms of what the result of this new design work will do for your business, and what will it do for your customers/end users. What does success look like?
What do you want me to produce? A website? Support material for a new product? A display or theming for a conference? Or do you want to refresh or totally reinvent your brand?
What insights do you have about the customers or users who will be exposed to your new design work? Who are they, what do they think of you and what might they expect of you? The more information you can provide about the typical customer or user, the easier it is for me to create something that will resonate with them. If you have research to guide you, share this.
If you can, paint a word picture of a typical customer. Make them real, give them a personality and not just straight demographics such as blue collar male, aged between 35 and 50. The more descriptive the better.
What other branded material does this piece of design work relate to and need to fit in with? Is it a new sub-brand that needs to be created or does it have to strictly adhere to some clear corporate identity guidelines? If so, make sure you provide your brand standards to the design company along with the brief.
If you have your brand story and your brand standards well articulated, then the tone and manner of any new piece of design work should reflect your 'voice'. If you don't have these resolved, then in the interests of future consistency of your design work, you should take some time to work through this.
Try and avoid words such as 'professional' (who wants to be unprofessional?), but use more evocative statements such as:- fresh, edgy, approachable, smart, etc. Doing this makes it much easier to evaluate the design work you are presented with.
Is there any other information that can help inform this brief?