When dealing with laws in the United States, it is helpful to remember that there are both state and federal statutes. For example, we have our own laws here in the state of Mississippi, but there are also federal laws that govern Mississippi as well. Persons who are accused of crimes may be accused in either state courts or federal courts. According to the Cornell Legal Information Institute, crimes that are considered federal crimes are generally laid out in Title 18 of the US Code.
There are several aspects to a crime which may cause the federal courts to have jurisdiction over the legal proceedings. For instance, the defendant crossing state lines during the course of the crime also makes the crime federal. For example, if a kidnapping occurs in the state of Mississippi and the kidnapper takes the victim to Arkansas, this would make it a federal crime.
If the crime takes place on federal land, then it becomes a federal crime. Federal land may include a US National Park, an Indian Reservation, or potentially a military base. Additionally, if the crime itself takes place across state lines, such as an interstate money laundering ring, this would make the crime federal.
Finally, if the crime involves US Customs or anything coming in over US borders, this automatically turns the situation federal.
There are also situations where both the state and the feds will have jurisdiction over the proceedings. Should this be the case, it is considered concurrent jurisdiction. It is possible for a defendant to be charged by both the state and the federal government for the same crime since they are considered separate offenses.