A corporate identity is, put simply, a symbol. It can be as simple as a colour scheme (e.g. orange and blue widely used in most of AOL's advertising) or a word written a certain way, (e.g. "Sony" written in those narrow, classy letters) or a picture (e.g. The Ship for Old Spice Aftershave.) These physical images are often associated with the "image" of the company behind them. They are designed with a certain motive. User Friendly for AOL, Sleek and High Tech for Sony, and Manly and Sturdy for Old Spice.
This is the basic idea of a corporate identity. When you see those images, not much else comes to mind. They are well recognized and those colour schemes, images, and words have been effectively used to bring those particular companies to mind.