Your brand is not your logo. Your brand is a combination of elements that communicate the personality of your business to your audience. A good way to simplify the concept is to divide a business into four areas: Product or service; Communications; People; Working environment. Each of these areas (and everything they contain) is your brand. What do each of these things say about you?
Your logo is part if your Visual Identity (which comes under the Communication heading in the list above). It's very visible, and very important, but it's just one piece of the brand jigsaw.
If you'd like to see some examples of logos that we have designed as part of brand development projects, visit www.alderandalder.co.uk and click on Design, then Identity.