If something is explained or defined in a new or different way, you can say it is a reinterpretation. If you see a rap version of Shakespeare's "Romeo and Juliet," that is a reinterpretation.
Reinterpretation has as its base the word interpret, which is from the Latin word interpretari, which means "explain or understand." If you are a detective working on a cold case, you have to reexamine the evidence. It is possible that you will catch something that others missed before, leading you to a reinterpretation of the case — and perhaps an arrest.