In one paragraph:
As consumers we buy based on our perceptions. This perception (what people think about your organization) is known as your brand. And our perceptions are shaped by the way we experience (through our senses) organizations via their materials known as their brand identity. These materials include everything we can sense: What we see, like brochures. What we touch. What we smell. What we taste. What we hear, like radio advertisements or the way you answer the telephone to the way you phrase your mission statement.
So, to sum up:
Brand Identity(business materials) shapes Perception and Perception determines sales(or buy-in, etc.).
Thanks Alina Wheeler.