The verb adjure is a heavy-duty synonym of the word "ask," with more of a demanding tone. For example, you might have to adjure someone to tell the truth.
You get a strong sense of the word adjure when you realize that the jure part is similar to "jury." Both come from the Latin jūrāre "swear," which in turn comes from jūs, jūr- "law" (as in justice and jurist). In 14th-century Middle English, the word suggested someone affirming something by swearing with an oath. So adjure means to command solemnly, as in "She adjured him to present the events precisely as he witnessed them."