Aspiration is not just about showing off.
Amazon describes The Business of Aspiration by Ana Andjelic this way:
"In the traditional economy, consumers signaled their status through collecting commodities, Instagram followers, airline miles, and busy back-to-back schedules. By contrast, in the aspirational economy, consumers increasingly convey status through collecting knowledge, taste, micro-communities, and influence. This new capital changes the way businesses and entire markets operate, and yet the modern aspirational economy is still an under-explored area in business and culture. The Business of Aspiration changes that."
While I don't agree that a brand is primarily about the user signaling status, I do find Andjelic's methodology helpful in understanding the underlying architecture of my own definition of a brand, as a way for an organization or company to signal to their end users how they serve them and their needs.
As an example, consider this recent blog post. In it she identifies signals to look for when predicting a brand's success by evaluating a sample of consumer brands according to the set of criteria grouped into four segments: culture, consumer, category, and company.
Article: The Brand Checklist