In the United States, a federal crime or federal offense is an act that is made illegal by U.S. federal legislation enacted by both the United States Senate and United States House of Representatives and signed into law by the president. Prosecution happens at both the federal and the state levels (based on the Dual sovereignty doctrine) and so a "federal crime" is one that is prosecuted under federal criminal law and not under state criminal law under which most of the crimes committed in the United States are prosecuted.
That includes many acts for which, if they did not occur on U.S. federal property or on Indian reservations or were not specifically penalized, would either not be crimes or fall under state or local law. Some crimes are listed in Title 18 of the United States Code (the federal criminal and penal code), but others fall under other titles. For instance, tax evasion and possession of weapons banned by the National Firearms Act are criminalized in Title 26 of the United States Code.