What does it mean to say the fifth amendment protects citizens against double jeopardy?

The Fifth Amendment to the United States Constitution provides that no person shall be subject for the same offence to be twice put in jeopardy of retrial after acquittal, conviction, multiple punishment, and or retrial after certain mistrial. Hence, in essence, this amendment protects a person getting into jeopardy again for the same offence which had initially led him into jeopardy.