A trademark (sometimes called simply a "mark") is any word, phrase, design, or symbol used to market a product or service. Technically, a mark used to market a service, rather than a product, is called a service mark, though the term "trademark" is commonly used for both types of marks because they refer to the same group of legal protections. Owners of trademarks have rights under both federal and state law that give them the power in many cases to prevent others from using the same or confusingly similar trademarks.
To make sure your proposed business name won't step on someone else's rights to an existing trademark, you'll have to do a trademark search. (Read Make Sure Your Proposed Business Name Is Available to learn how to do a trademark search.) Also, when picking a business name, you should take care to choose a name that will be likely to receive trademark protection and then take steps to protect your business name as a trademark. For more information on names that are likely to receive trademark protection, see Pick a Winning Name for Your Business, and for more information on protecting your business name as a trademark, see Filing a Federal Trademark Application FAQ.