The state action requirement refers to the requirement that in order for a plaintiff to have standing to sue over a law being violated, the plaintiff must demonstrate that the government (local, state, or federal), was responsible for the violation, rather than a private actor.
This requirement only applies when the law in question requires the government to have acted.
This state action requirement extends to a number of actions.
According to the Supreme Court in Edmonson v. Leesville Concrete Co., Inc., 500 U.S. 614 (1991),"Although the conduct of private parties lies beyond the Constitution's scope in most instances, governmental authority may dominate an activity to such an extent that its participants must be deemed to act with the authority of the government and, as a result, be subject to constitutional constraints."
First Amendment
The First Amendment states that “[c]ongress shall make no law” infringing upon the freedoms of speech and religion. Because of this requirement, it is impossible for a purely private party to violate this Amendment.
Discrimination
In Edmonson, the Supreme Court wrote that "discrimination, though invidious in all contexts, violates the Constitution only when it may be attributed to state action."
Further Reading
For more on the state action requirement, see this Cornell Law Review article, this University of Missouri Law Review article, and this Harvard Law Review article.