What's your interpretation of X? asks you to say what you think X means. What's you explanation of X? asks you to tell me something that will help me understand X.
An explanation is the logical (non-contradictory) arrangement of facts translated into a simpler language. An example of this is a scientific theory that has been tested and proved. Its general rule is to be simpler than the phenomenon itself (Remember Occam's Razor: "entia non sunt multiplicanda praeter necessitatem", or "entities should not be