The lawsuit in Trump v Vance was over the constitutionality of a state grand jury request for records from President Trump's accountants.
So with that in mind, what exactly is a grand jury and how do they work?
- Wikipedia: Grand juries in the United States.
Grand juries in the United States are groups of citizens empowered by United States federal or state law to conduct legal proceedings, chiefly investigating potential criminal conduct and determining whether criminal charges should be brought. The grand jury originated under the law of England and spread through colonization to other jurisdictions as part of the common law.
. . . Generally speaking, a grand jury may issue an indictment for a crime, also known as a "true bill," only if it finds, based upon the evidence that has been presented to it, that there is probable cause to believe that a crime has been committed by a criminal suspect. Unlike a petit jury, which resolves a particular civil or criminal case, a grand jury (typically having twelve to twenty-three members) serves as a group for a sustained period of time in all or many of the cases that come up in the jurisdiction, generally under the supervision of a federal U.S. attorney, a county district attorney, or a state attorney-general, and hears evidence ex parte (i.e. without suspect or person of interest involvement in the proceedings).
. . . In the early decades of the United States grand juries played a major role in public matters. During that period counties followed the traditional practice of requiring all decisions be made by at least twelve of the grand jurors, (e.g., for a twenty-three-person grand jury, twelve people would constitute a bare majority). Any citizen could bring a matter before a grand jury directly, from a public work that needed repair, to the delinquent conduct of a public official, to a complaint of a crime, and grand juries could conduct their own investigations. In that era most criminal prosecutions were conducted by private parties, either a law enforcement officer, a lawyer hired by a crime victim or his family, or even by laymen. A layman could bring a bill of indictment to the grand jury; if the grand jury found there was sufficient evidence for a trial, that the act was a crime under law, and that the court had jurisdiction, it would return the indictment to the complainant. The grand jury would then appoint the complaining party to exercise the authority of an attorney general, that is, one having a general power of attorney to represent the state in the case. The grand jury served to screen out incompetent or malicious prosecutions. The advent of official public prosecutors in the later decades of the 19th century largely displaced private prosecutions.
For more:
Findlaw: How do Grand Juries Work?