A long arm statute is a law passed by a state legislature
to grant the state's courts personal jurisdiction
over residents of other states.
To understand what long arm statutes are about, it's important to understand how the concepts of federalism and due process are intertwined in the United States.
Federalism, in a nutshell, is the concept that the national government of the United States (that is, the U.S. federal government) exists in parallel with quasi-autonomous state governments. The Constitution gives the federal government power to pass laws in certain areas—national defense, interstate commerce, and the like. Everything that isn't given to the feds in the Constitution, or banned outright to everyone by the Constitution, is up to the states to sort out for themselves... which is why we have gay marriages in Massachusetts, medical marijuana in California, and Long Island Iced Tea delivered in multiple shotglasses in Utah.
One consequence of federalism is that Americans have a weird sort of dual citizenship. The Fourteenth Amendment, among other things, stipulates that people are citizens of the United States by birth or naturalization, and simultaneously citizens of the state in which they reside. A person is a "citizen" of the United States as a whole while they are a "resident" of one of its states. If they leave the state where they reside, they take on a halfway-foreign national status.
Which brings us to due process. Due process is mentioned in the Constitution and defined in different ways, but it generally means that the government has to be reasonably fair when a person's life, liberty, or property are going to be taken: or, in other words, the government owes the accused the ability to defend themselves by means of some process.
If a person lives in Florida and has never left the state or had contact with people outside the state, it sounds very unfair to force them to travel to Hawaii to defend themselves, just because someone in Hawaii sued them in a Hawaiian court. So it is said that the government of Hawaii has no "personal jurisdiction" over a Floridian, unless the Floridian happens to be in Hawaii or has an agent to represent them in Hawaii. (This standard was established by a United States Supreme Court case, Pennoyer v. Neff, in the 1800s.) Now you can see the problem: if the Hawaiian wants to sue the Floridian, they have to go all the way to Florida.
This wasn't a big deal when interstate interactions were very limited, but as time passed, it eventually became quite a big deal.
The origins of long arm statutes
The main reason for the development of long arm statutes was the automobile. Cars are easy to drive from state to state, and often start lawsuits when they crash into each other. Indeed, the 1969 edition of Ballantine's Law Dictionary defines "long arm statute" as "a statute providing for constructive or substituted service of process on a nonresident motorist." Nowadays, long arm statutes have been expanded beyond motorists to include many classes of corporations and private individuals.
But you can picture the basic scenario: A person drives their car from New York to Florida. In Florida, they get into an accident. Some time later, after they've returned to New York, they are sued by the Floridian who they ran into. So where should the suit take place? In the absence of a long arm statute, the suit has to take place in New York. Floridian courts do not have personal jurisdiction over New Yorkers unless they are in Florida, and since the New Yorker in question is not currently in Florida, a Floridian court cannot summon them to answer the plaintiff's complaint.
So long arm statutes were born.
There are several ways to extend a state's jurisdiction to non-residents. The simplest is to allow service of process beyond the state's boundaries. When a lawsuit is started, the plaintiff is responsible for having their complaint delivered to the defendant, usually by a courier known as a "process server." To extend their jurisdiction, some states passed statutes recognizing the validity of process served outside the state. Other states set up a system where the plaintiff would serve process on a registrar, who would then notify the out-of-state defendant by mail and send them a copy of the complaint.
Besides automobile accidents, long arm statutes became important in a number of cases. Corporations, for instance, often do business in states where they are not incorporated. Often, they do business in states where they don't even have offices or permanent contacts. So long arm statutes were extended to cover nonresident corporations as well as motorists. From there, it was a simple leap to include private citizens doing business in states where they didn't reside.
The constitutionality of long arm statutes
As you might have guessed by now, long arm statutes do not go down well with people who would rather be sued close to home (if at all). A number of constitutional challenges have been mounted against these laws, usually on the basis of the Fourteenth Amendment.
In the 1927 case of Hess v. Pawloski, the United States Supreme Court ruled that Massachusetts' long arm statute was constitutional. The statute provided that any out-of-state motorist could be sued in Massachusetts for acts they committed while driving in Massachusetts; process would be served through a registrar. In its reasoning, the Court drew on the concept of freedom of movement. If motorists could not be sued when driving outside their home state, it would induce states to keep non-residents from driving. This was already a problem in corporate law: corporations had to designate agents to receive process in every state where they operated. The Court concluded that an expansion of personal jurisdiction to cover out-of-state motorists was completely reasonable and not violative of due process, as long as it kept the state government from discriminating against non-residents. Implicit in this idea was that a person had to be present in a state at some point in order to be subject to that state's jurisdiction.
This power did not go unqualified, however. In 1945, the Supreme Court refined its view in the case of International Shoe v. Washington, where the state of Washington had served process by mail upon a company in St. Louis for not making payments into a state unemployment compensation scheme. (The company employed some salesmen in Washington but had no office there.) Reasoning that a corporation had no physical presence other than its employees, the Court adopted a "minimum contacts" standard. As long as a corporation had "systematic" contact with a state, as opposed to "casual" or "incidental" contact, it could be subject to the state's long arm statute without raising any due process issues.
Since then, this "minimum contact" standard has been applied and re-applied to many cases. The area where it raises the thorniest problems is in product liability claims. A person could buy a car in New York, drive it to Oklahoma, and then sue the New York dealer in Oklahoma if a defect emerged. Would the Oklahoma long arm statute apply in this case? The Supreme Court said no in World-Wide Volkswagen v. Woodson (1980), since there was no contact between the dealer and the state of Oklahoma besides a random customer driving their car across the country.
But suppose that a factory in Ohio produced a faulty part which ended up in a water heater built in Ohio and sold by an Illinois dealer. Could an Illinois consumer sue the Ohio factory in an Illinois court over a defect in that part? Although the U.S. Supreme Court did not decide this question, the Illinois Supreme Court did decide, in Gray v. American Radiator (1961), that manufacturers had "minimum contacts" with end users of their products, even if there were middlemen making interstate transactions along the way.
Generally speaking, a choice of jurisdiction must balance three competing interests: the state's interest in serving as a venue, the plaintiff's interest in filing suit there, and the defendant's burden in answering suit there. This means that the plaintiff and defendant must both have a legitimate connection to the venue, and the state must have a legitimate reason to be the venue. So if, for instance, a Taiwanese corporation tries to bring a Japanese supplier to court in California when the Japanese supplier has never done any business in California, the exercise of jurisdiction is probably unreasonable no matter how California feels about the matter. Yes, this was a Supreme Court case, too: Asahi Metal Industry v. Superior Court (1987).
Choice of jurisdiction is usually based on where the defendant resides, or where the act in question took place. But say the defendant is a big company with operations in every state, or a Donald Trump-like individual who's everywhere at once. And say that the act in question isn't really tied down to a place: something like libel, where the act occurs in many places at once. What jurisdiction then?
In cases like these, plaintiffs and their lawyers can sometimes use long arm statutes to hand-pick their favorite jurisdiction. There are logistical considerations that can preclude this sort of activity: for instance, individual lawyers cannot practice in a state without being admitted to the bar there, and a plaintiff will not naturally want to file suit in a far-away land when they can file suit close to home.
But under certain conditions, tactical use of long arm statutes can be productive. States have different laws. An act might be legal in one state, but illegal in another. Courts in one state might be more amenable to rule for the plaintiff than courts in other states. Or, if the suit is touching an aging issue, there might be only a few states where the statute of limitations will allow a suit. Although this sort of tactic can be risky if the judge smells something amiss, states will generally allow suits to be brought across vast distances as long as the plaintiff's interest, state's interest, and defendant's burden seem to reach a decent equilibrium, and as long as all the parties involved have the requisite minimum contacts with the state.