Branding in one word is perception. It is basically how people see you. Following this pattern, brand identity is how a business presents itself and want to be perceived by the customers.
Be consistent when building a brand, and know your target. Your aim of branding is successful when people see you the way you want them to see you.
Branding encompasses name, logo, colour, shapes, ads, language and interaction with customers. A good branding creates trust, and will make people pay more.