Avery with ECI discusses what professional insurance is. Professional insurance is also known as E&O, errors and omissions insurance or medical malpractice insurance. Professional insurance is going to cover you and your business for doing professional acts. It's going to cover you if the person you're working with suffers financial harm due to mistakes on your part, that's the errors, or if you fail to perform a service, that's the omission. It's going to cover you in civil court, but you need to be aware it's not going to cover you for criminal acts.
Avery goes into greater detail in her article Professionals in a Professional World.