Amtrak is the United States's national passenger railroad company. Its full name is the National Railroad Passenger Corporation, and "Amtrak" is short for "American Travel by Track". Its original short name, "Railpax", sounded too much like a political action committee.
Amtrak was created as a bailout of intercity passenger service in 1971. The railroad companies back then had gone into decline, being beset by taxpayer-financed competition, awkward regulations, and stubborn labor unions. The bankruptcy of the Penn Central seemed like a harbinger of the fate of the US railroad industry. Even worse, passenger service was not making them much money, if any. So instead of subsidizing or mandating the railroads' passenger service, someone had the idea of a creating a government-owned corporation that would take over passenger service. Thus, Amtrak.
Nobody expected Amtrak to survive very long, not even its management, but it did. However, it has continued to be dependent on subsidies, something that makes it get labeled "wasteful government spending". Nevertheless, it has gotten enough money over the years to have bought most of its present rolling stock and to extend electrification from New Haven to Boston.
Amtrak also has the problem that owns only a little bit of the trackage that its trains travel on, mostly in the northeast. In most other places, Amtrak runs on the tracks of the railroads that formerly provided passenger service, and that are now exclusively in the freight business. This means that Amtrak trains sometimes get stuck on passing sidings, waiting for freight trains to pass.
There are several types of Amtrak service.
The Northeast Corridor is Amtrak's busiest line. It runs Boston - Providence - New Haven - New York City - Trenton - Philadelphia - Wilmington - Baltimore - Washington, DC, with branches to Harrisburg and Hartford. The Boston-DC and Philadelphia-Harrisburg lines are the only electrified intercity lines in all of North America, though some cities have partially or completely electrified commuter-rail systems. The NEC is also the home of Amtrak's fastest trains, the Acela. The NEC likely helps keep Amtrak going by being ridden by many Washington decision makers, like Joe Biden.
There are several state-supported regional corridors, in places like California, Washington State, Oregon, Illinois, Michigan, North Carolina, Virginia, New York State, Vermont, and Maine, with lines running over much of the length of those states. Some of them are rather busy, running over 10 trains per direction per day.
There are also several long-distance lines, lines extending over much of the size of the contiguous United States through several states. These usually have 1 train per direction per day, and sometimes fewer. The long-distance lines also help Amtrak because of their pork-barrel value. By extending into nearly all of the contiguous states, they help create pro-Amtrak lobbies in nearly every state.