Elena was a prince's daughter who shared the same feelings towards certain things as Daemon. Daemon said that her smile was like the sun and she soothed him like the moon. She introduced Daemon to the first Vongola boss, Giotto.
Daemon gave the Vongola everything he had for Elena, and she said that she thought the Vongola Family, protectors of the weak and defenseless, was Daemon's pride.
When Giotto threw away his military forces to prevent "fighting for self interest", a rival Mafia family invaded their territory and wounded Elena, who died shortly afterwards. After Elena died, Daemon swore to make the Vongola strong in Elena's name.
Daemon, to keep his promise threw away his body, and kept watch over the Vongola through the generations, and always stamped out the weak, in order to make the Vongola strong.
Source: Reborn Wiki