The United States of America is considered to be a representative democracy because American citizens elect officials serve as their representation in government. For example, a U.S. Senator. There are 100 Senators, 2 Senators representing each of the 50 States. Those Senators are elected by the inhabitants of their state for one reason; and that's because they will represent those inhabitants in government. This is why campaigning and appealing is so crucial to winning elected office; you want people to entrust you with the task of representing them.
A simpler way to imagine a representative democracy is like this:
Citizen ⇒ Representative ⇒ Government
The concept of a direct democracy differs from that of a representative democracy because unlike above, in which there is a "middleman" between the citizens and the government, there is no middleman in the case of a direct democracy. That is why it's "direct."
