The myths of Echo and Narcissus are wonderful and do have a moral lesson. Let me first give a short summary.
Echo was a beautiful nymph that loved to talk. One day, Hera was looking for her husband, and Echo believed that he was flirting with the nymphs. So, she held Hera up with her chatter to protect her friends. Hamilton writes:
However, [Hera] was immediately diverted from her investigation by Echo's gay chatter.
When Hera realized what Echo was doing, she cursed her. Echo could have the last word but no longer had the power to speak first. The big problem was that Echo loved the youth Narcissus, but Narcissus scorned all the nymphs, including Echo. In great sadness, Echo pined away to nothing but a voice. As for Narcissus, the nymphs prayed that he would fall in love with one who does not love him. This actually did happen when he fell in love with his own reflection in a pool of water. He, too, pined away and died.
The lessons are twofold. The first is to fear the gods and not cross them as Echo did. It is important to keep in mind that the Romans believed that they were the most pious people on earth. Second, do not act cruelly towards others lest that cruelty turn back on you.