Representative characteristics are when you elect someone to represent you and make desicion and laws for you, a direct characteristic is when you can directly make laws and changes to regulations, in this case many countries have both, where you can gather signs and unite people to pass a law or ask for one and can also elect senate and presidents in order to represent you.
In the United States, we have a democratic type of system that is both representative and direct. The representative element includes when we citizens elected officials for different offices. This includes the presidency, members of the US Congress, state representatives, etc.
However, many states in the US allow for direct participation in which citizens can propose and pass legislation without government approval. An example of this would be a ballot initiative. A ballot initiative allows citizens to gather signatures on a measure that they want to become law. If enough signatures are gathered, this piece of legislation is then voted on by the citizens. If the legislation passes, it becomes law without the help of the state or federal government.