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!