The more common definition of a brand, as it is used today, is the use of it by corporate America to distinguish a product. Coca Cola is a kind of soft drink. McDonalds? is a kind of fast food. Kleenex? is a kind of facial tissue.
Branding, in corporate America, ultimately seeks to establish what is called "mind share." Mind share is the status a brand can achieve when it co-exists with deeper, more empirical categories of objects. Kleenex, for example, can distinguish itself as a type of tissue. But, because it has gained mind share amongst consumers, it is frequently used as a term to identify any tissue, even if it is from an opposing brand.
Mind share can be established to a greater or lesser degree depending on product and market. In Texas, for example, it is common to hear people refer to any soft drink as a Coke, regardless of whether it is actually produced by Coca Cola or not.
A legal risk of mind share is that the name can become so widely accepted that it becomes a generic term, and loses trademark protection. Examples include 'escalator' and 'mimeograph'. 'Aspirin' is a special case--the US government took the trademark away from Bayer during the first World War, not because the term was being used generically, but as "enemy property," because Bayer is a German company.
Branding and Mind Share are successful tools for the marketing of a product.
They are also at the heart of what non-American countries refer to negatively as "Americanisation".
Brands (American):