There are few sadder phrases than those two little red words your iPhone displays when a message fails to send: "Not Delivered." Those words, along with that exclamation point in a circle, mean your charming photo or witty comment didn't go through.
Fortunately, as in life, with the iPhone: the simplest answer is usually the correct one. If your iPhone is not sending messages, first make sure you have a connection to either a Wi-Fi or cellular network, and make sure your phone is not set to Airplane Mode.