1. The young man was accused of a terrible crime. His parents were convinced that he was innocent and swore they would move heaven and earth to get him acquitted.
2. Linda’s daughter is getting married on Friday, the same day Linda gets back from an out-of-town business trip. She will move heaven and earth to get to the wedding on time.

The expression suggests how hard one would have to try if one tried to move things as big as heaven and earth.