Without Googling it. How would you Define Brand?

Simply put, a brand is the "personality" of the company. it's how they communicate with the outside world and also their employees, their principles, how they visually "look", the way they do everything.
A brand personifies a company.

Expectation & Experience

the 1st thing thoughts and emotions people have when they read or hear about your company

Shorthand for trust.

Story. Your story. The story you tell.

"Brand is the distribution of likely outcomes that you can expect from any company or person." —Brent Beshore

It’s the clearest explanation I’m aware of. In fact, I recently shared it on Twitter.

The differentiating identity of a product or service.

A brand is an image of a company, perceived by consumers emotionally and rationally. It's supposed to be cool, so that its target audience can relate to the set of values that it comes across as having. That image is created through the process known as branding :P Well-done branding includes PR activities and well thought-out designs. A brand is something that people like love and want to be part of.