Immigration and Naturalization Service was a federal agency that primarily dealt with enforcing laws related to immigration and naturalization. This agency was a part of the Department of Justice. However, in 2003 this agency was formally dissolved. It was absorbed by the Department of Homeland Security and now several other federal agencies are responsible for dealing with immigration and naturalization laws.
There are many laws related to non-U.S. citizens coming into the country. There are laws about these people gaining citizenship, laws about how they can enter the country, laws about the behavior that is expected of them, etc. A federal agency is needed to enforce these laws, and to otherwise oversee this area of government. Immigration and Naturalization Services used to be largely responsible for this. However, this is no longer the case.