Products typically fall into categories. Hertz is in the rental car category. Toyota is in the car category. Symantec is in the security software category. Xerox is in the copier category. Categories, at least to the extent they are relevant, exist inside in the minds of consumers.
The most powerful position for your brand to occupy is to be synonymous with a category. If your brand is synonymous with a category, it means that people automatically think of your product when they think of the category, and vice versa. They don't think about the competition.
If possible, you should strive to create a new category and have the first and only product in it. Remember, though, categories exist in the mind. So you have to create your new category in the mind.
Stay tuned for more on categories and how your marketing can affect them.