"est" is only "is" in an affirmative sentence. In French, to ask a question, you need to invert the subject and the verb (like "il est" becomes "est-il ?") or you can use a question marker (expression or word that tells you are indeed asking a question) "est-ce-que" is one of those expressions. It doesn't just mean "is" now that it's tacked with the other 2 words, it means "?" And sometimes it doesnt mean "is" at all. For example, "est-ce que je peux venir ? means "Can I come ?"
So in your example, it means "is my shirt green".