What is a Brand?
A corporate identity is a big part of a brand so to know what a corporate identity is, means to know what a brand is.
A brand is not a business. A brand is not a product. A brand is also not the name of a business or a product. And contrary to the belief of many, it is also not just about the look of a business or a product.
One common definition is that a brand is the sum total of how someone perceives a particular organization. (Ashley Friedlein)
Another definition many marketers and designers agree on is the definition of David Ogilvy who suggested in "On Advertising" that a brand is:
"The intangible sum of a product’s attributes: its name, packaging, and price, its history, its reputation, and the way it’s advertised." - David Ogilvy
This definition is closer to the "official" definition of the American Marketing Association which claims a brand is:
A name, term, design, symbol, or any other feature that identifies one seller’s good or service as distinct from those of other sellers. The legal term for brand is trademark. A brand may identify one item, a family of items, or all items of that seller. If used for the firm as a whole, the preferred term is trade name. - AMA
But in reality, there is no unifying definition of a brand, it is subjective and transformative. It always changes and so does its definition.
However what is agreed on in general is that building a brand is one of the most important quests in marketing and to properly do that the most important part, besides the product itself, is the Corporate Identity.