Direct Democracy: In this form of Democracy, the citizens have the right to "rule" and set up all laws and what the course of what the government takes. They have a "direct voice" in the government, hence "direct democracy". An example of this is Ancient Greece, which allowed each citizen to voice their opinion and vote for what they believe.
Indirect Democracy: In this form of Democracy, the citizens do <em>not</em> have the right to directly "rule". Instead, they have the power to vote for politicians that have the same beliefs as the supporting voters, who will push for the change the voter's want. An example of this is the United States of America, which allows citizens to vote for legislators, who then creates and tries to pass the rules the voters want.
