To prosecute is to participate in or pursue something to completion, like a government’s intention to prosecute a war. Prosecute is most often used for bringing legal action against an accused person or group.
Prosecute comes from the Latin, “prosesutus,” meaning “follow after.” The legal sense of the word first appeared in the 1570s. A district attorney will often prosecute, by bringing legal charges and action against a person or group (watch any TV legal drama, and the prosecution will no doubt prosecute eventually). A company may prosecute by suing to protect against damages. Prosecute should not be confused with the word persecute, which means to harass or oppress.