There are many ways in which one could explain the US political system. If you have a more specific question that comes to mind as you read this answer, please let us know. The US system of government is a republican system that is mainly set up in such a way as to make it as difficult as possible for the government to do anything that would infringe on the rights of the people.
The US government is republican. That is essentially the same thing as saying that it is democratic. However, it means that it is not much of a direct democracy. Instead, people elect officials to represent them.
The US government is set up so that these elected officials will have a very hard time infringing on the rights of the people. First of all, there are explicit limits on what government can do. This can be seen, for example, in the Bill of Rights. In addition, however, the system is set up to make government unwieldy. The government has separation of powers so that no one branch of government has all of the power. It has checks and balances so that all of the branches have to agree before anything very important can be accomplished. This all means that more parts of government must agree before any major laws can be passed.
In these ways, the US has a republic in which great pains have been taken to protect the rights of the people.