When people use the term, they generally mean:
Representative democracy is a variety of democracy founded on the principle of elected people representing a group of people, as opposed to direct democracy. [Wikipedia]
Is the goal for each representative to vote the way that the people they represent would vote if they had the time/energy/education to study the issue, or the way that they feel is "better"?
Additionally, is their duty primarily to those that elected them, or to the country as a whole (ex. Does the congressman from Alabama have an obligation to do what is best for the country or for his state should there be a conflict)?