The case of US v. Lopez has to do with the power of the US Congress to make laws under the Commerce Clause. It is a case about federalism.
According to the US Constitution, the US Congress cannot simply make laws that dictate how people can live within the various states. The Constitution says that the federal government has some powers and state governments have other powers and that neither side can take powers meant for the other. Lopez is a case in which the Supreme Court said that the US Congress had gone too far and had illegally taken power from the states.
Lopez was arrested for bringing a gun to school. He was convicted under a federal law that made it illegal to possess guns near schools. He sued, saying that the federal government had no right to make such a law. He said that the state government was the one that had a right to make such a law.
The US government claimed that it had a right to make such laws under the Commerce Clause of the Constitution. This clause says that the Congress can make laws regulating commerce between the states. This clause has been used to justify many kinds of federal laws. This is, for example, why Congress has the right to ban racial discrimination in places like restaurants. The idea is that the restaurant is part of interstate commerce and so the Congress can make laws that govern it. In the Lopez case, the US government said that having guns in schools would hurt the economy and that it, therefore, had the right to ban them.
The Supreme Court disagreed. It said that there was not really any connection between interstate commerce and this law. Therefore, it said that Congress did not have the legal right to make the law under which Lopez was convicted. This was the first time since the New Deal era that the Supreme Court said that there were limits on the kinds of laws that Congress could make under the Commerce Clause.
(Please note that, although this case was about guns in schools, it has nothing to do with the Second Amendment, which is a big issue these days.)