A brand is a shorthand for the customer’s expectations. What promise do they think you’re making? What do they expect when they buy from you or meet with you or hire you? That promise is your brand.
Seth Godin • This Is Marketing: You Can't Be Seen Until You Learn to See

A brand is not ‘a logo’, nor is it even strictly ‘design’. A brand is an experience, a feeling, a sense and a vibration that oozes out of every interaction (however fleeting) between your business and a prospective client.
Liam Veitch • Stop Thinking Like a Freelancer
Brian Collins • 101 Design Rules
I believe that “brand” is a stand-in, a euphemism, a shortcut for a whole bunch of expectations, worldview connections, experiences, and promises that a product or service makes,
Debbie Millman • Brand Thinking and Other Noble Pursuits
decide what ‘image’ you want for your brand. Image means personality. Products, like people, have personalities, and they can make or break them in the market place. The personality of a product is an amalgam of many things – its name, its packaging, its price, the style of its advertising, and, above all, the nature of the product itself
David Ogilvy • Ogilvy on Advertising
A brand is also far more than the name, logo, symbol or trademark that highlights its origin; it is imbued with a set of unique values that defines its character and works as an unwritten contract, promising to deliver satisfaction by providing consistent quality each time it is bought, used or experienced.
Catharine Slade-Brooking • Creating a Brand Identity: A Guide for Designers: (graphic Design Books, LOGO Design, Marketing)
A brand is a shorthand for the customer’s expectations. What promise do they think you’re making? What do they expect when they buy from you or meet with you or hire you? That promise is your brand.