A brand guideline is a document which outlines the rules of your brand. If you've got a brand and you want to ensure it is always re-produced in a way you'd be happy to see it being used, then brand guidelines can help you to provide those trusted with using your brand to get it right ever time.
The way your brand is portrayed by those that use it affects the way people view your business and your brand. So - if your brand is being used by partners who aren't using the right typeface or the correct colours that your branding was designed in, you'll be sending mixed brand messages. This inconsistency is confusing. A brand represents who you are and the values you stand for. If you send mixed messages then your reputation might not be as clear as it could be.
A big part of brand guidelines is logo reproduction. Logos can be produced in a series of formats - EPS, AI, tiff, jpeg - depending on the media. There can also be different logos for different types of printing job. If you're printing in spot colour, your colour scheme could have certain pantone colours. If you're printing in full colour process (CMYK) then the levels of CMY and K should be consistent for each colour you use. You can also have a black and white version to ensure that when your logo is used in black and white that it reproduced properly. If not, people may use your colour version of your logo which might appear as varying shades of grey.
For example - if part of your logo contains yellow text and someone prints it out in black and white - they will effectively be printing a light grey which might not be readable. If you provide a black and white version, you might specify 50% black or 100% black to create the right contrast to make it readable.