A more thorough explanation:

Vance v. Terrazas is a legal case that was decided by the United States Supreme Court in 1980. The case dealt with the issue of expatriation, which is the process of giving up one's citizenship. The court held that the U.S. government must prove intent to surrender U.S. citizenship and not just the voluntary commission of an expatriating act. The appropriate standard of proof for analyzing the citizen’s conduct would be proof by a preponderance of the evidence.

For example, in the case of Laurence Terrazas, he was born in the United States to a Mexican father. While attending a Mexican University, Terrazas applied for a certificate of Mexican nationality. In this application, he was required to sign a statement renouncing his U.S. citizenship, which he did. During a later interview with a U.S. consular officer, Terrazas gave conflicting answers to whether he intended to give up his U.S. citizenship when he applied for Mexican nationality. The State Department eventually concluded that Terrazas had lost his U.S. citizenship. Terrazas appealed, and the Supreme Court established that a U.S. citizen cannot be expatriated without his or her assent.

The Court also held that it is permissible for the government to have a rebuttable presumption that the expatriating act was committed voluntarily. This means that the burden of proof is on the individual to prove otherwise, such as duress, etc. If the individual succeeds, there would be no expatriation, but if he fails, then the question still remained whether all the evidence the government had satisfied its burden of proof that the expatriating act was performed with the necessary intent to relinquish citizenship.