When you say "What the period is" you make a statement: What ___ is. When you say "what is the period" you ask a direct question: What is ____. "This is the best way to explain" is a statement, so it belongs with the statement "what the period is". However, even if you were asking a question, "What is the best way to explain..." you would still use the statement "what the period is" so the sentence wouldn't have a question inside a question!

This is the best way to explain what the period is. There is no reason to have an inversion of the subject and verb here, so your second version wouldn't be correct.