As Jeff Bezos says, "Branding is what people say about you when you're not in the room." Your product leaves an impression on your customers long after you've made the sale. Brand identity is the process of shaping that impression.
For all intents and purposes, your brand's logo is the "face" of your business. But that face should do more than just look cool or interesting -- a logo's contribution to brand identity is associative, too. It tells the public that [this image] means [the name of your company].
Having a brand identity doesn't just make your product more memorable; it makes your brand more authoritative in the marketplace. A brand that establishes a face, and maintains that face consistently over time, develops credibility among its competitors and trust among its customers.