One of the best explanations of branding I've ever seen was in a New York Times article, The Brand Underground, by Rob Walker. Here it is:
"Branding is ... a process of attaching an idea to a product. Decades ago that idea might have been strictly utilitarian: trustworthy, effective, a bargain. Over time, the ideas attached to products have become more elaborate, ambitious and even emotional. This is why, for example, current branding campaigns for beer or fast food often seem to be making some sort of statement about the nature of contemporary manhood. If a product is successfully tied to an idea, branding persuades people -- consciously or not -- to consume the idea by consuming the proudct. Even companies like Apple and Nike, while celebrated for the tangible attributes of their products, work hard to associate themselves with abstract notions of nonconformity or achievement. A potent brand becomes a form of identity in shorthand."
There it is folks. Print this one out and stick it on the wall. Branding is a process of attaching an idea to a product. (or service). It's not a logo. Period. Full stop. [I know -- I'm preaching to the converted here, but wasn't that a beautiful expression of the idea?]