A corporate image is a visual signature/profile for a business or corporation.
When I did some design work for a major college I was sent a form that listed the campus mascot, all versions of the campus logos, the campus colors, and details as to when, where and how they were to be used. This was to maintain their corporate image.
In addition a corporate image can include fonts that are to be used in conjunction with your logo and exact sizes that your logo may be printed.

How would my company benefit from a corporate image?

When a potential customer sees a company that presents itself in a consistent professional manner, they recognize that company and are more likely to deal with that company.
You walk past a Coke™ or a Pepsi™ machine you don't even have to read it to know what is being sold. Even if you didn't stop to buy anything you just in the back of your mind thought Coke™ or Pepsi™. This is due to corporate image.
If you receive a letter from a company and it's on plain white paper with a black and white logo poorly printed in the corner you wonder to yourself about the validity of the company and you are more likely to take your business elsewhere.