Understanding Cross-entropy Rubik's Code

A couple of days ago a friend of mine, who started exploring deep learning, asked me "Hey man, can you explain this Cross-entropy thing to me?". Now, that is a tough question, because this topic is never set with me right. My self-doubt kicked in, so in my mind, this question actually sounded more like "Can you explain Cross-entropy to yourself?". Even in my conference talks, I usually avoid mentioning it. Every time I start talking about it, I get all confused and convoluted.