Echo and Narcissus
This is a story we know mainly because Ovid wrote it down in his poem, the Metamorphoses. It's a traditional Greek story - there are illustrations from Greek vase painting about 500 BC - but Ovid's is the best known version.
In this story, Narcissus was a very beautiful young man who was very beautiful, and everyone admired him. He started to admire himself, too, and he was always going and looking at his beautiful reflection in puddles and ponds (there weren't any glass mirrors yet, and it's hard to see yourself well in a polished metal mirror). Narcissus was so beautiful that people were always falling in love with him. He got so used to everyone falling in love with him that he started to treat them badly - he would make fun of people who cared about him, and be mean to them. One girl in particular, the nymph Echo, fell in love with Narcissus, but he didn't care about her - he told her to get lost. Echo followed him around, sadly repeating everything he said, but she gradually faded away out of sadness, until only her voice was left - the echo you can hear in valleys today.
Narcissus' rejection of Echo is a form of hubris: Narcissus was acting like a god, who people should worship, but he wasn't really a god. The gods didn't like Narcissus acting this way. They decided to punish his pride, as in our proverb, "Pride goes before a fall."
So the gods made Narcissus fall in love with his own reflection when he went to admire himself in the pond. Because of the gods' enchantment, Narcissus was so much in love with his own reflection that he couldn't bring himself to leave the pool, and he just stayed there, admiring his own reflection, until he starved to death (or in some other versions, until he realized it was hopeless and killed himself with his own sword).
Narcissus is the name of a kind of daffodil (it's actually a pre-Greek word, passed down from the people who lived in Greece before the Greeks arrived), and Greek and Roman people pointed to these daffodils and said they were the soul of Narcissus, still standing by the pond, admiring his own reflection.
You can read more Greek stories about hubris: the story of Niobe which is also in Ovid, or the story of Arachne, who got turned into a spider, or the story of Tantalus. How are these stories the same?