Who has the power to judge another person's guilt/innocence/life? A judge? A jury? Why? How does one acquire the power, the right to judge another?

A jury has the power to judge another person's guilt/innocence/life.

A jury is a sworn body of people convened to render an impartial verdict officially submitted to them by a court, or to set a penalty or judgment. Modern juries tend to be found in courts to ascertain the guilt, or lack thereof, in a crime. The old institution of grand juries still exists in some places, particularly the United States, to investigate whether enough evidence of a crime exists to bring someone to trial.