Willful infringement occurs when the user of a mark knows or should have known that the mark was already being used by another. While a willful infringement defendant is liable for monetary damages, an innocent infringer can only be forced to stop using the mark.
Willful infringement is presumed (though can be rebutted) when the mark that is infringed is federally registered. Furthermore, recent court decisions suggest that the user of a mark may be deemed to be a willful infringer if they fail to conduct a reasonable search of existing similar trademarks prior to adopting a mark.