I highly recommend the book Making Meaning by Diller, Shedroff & Rhea (2006). The material is well researched and built from significant insight and a good deal of hard data. The core question of the book is what meaning is being produced through interaction with a brand.
From this perspective, the production of meaning can be understood as a key or even primary goal of the brand interaction.
Of course meanings can be significantly culturally-bound. However, they identify a number of meanings which appear to be cross-cultural. Not meant to be an exhausting list, it is nonetheless interesting.
Which one of these meanings could be considered vitally important and even understood as the primary goal of your brand?