"A brand exists in your mind. It's a collection of associations or feelings people have about a particular product, service, or an organization. Branding is the tangible process of creating the signals that generate these associations."
-- Allen Adamson, "BrandSimple"
This is an interesting tautolgy sometimes forgotten.
Indeed a strong brand is product of a good, effective and relevant (ideally) branding process, capable of triggering diferent but spontaneous associations in people's heads.
Ex: Apple = white + minimalist + apple logo + design + Mac + innovation + solutions + iPod + iPhone + iTunes + music + different from the herd + urban cool + Steve Jobs + "rule breaker" ...