Orpheus- The protagonist of this myth is Orpheus. Orpheus was a lyre player. His father was Apollo and his mother was one of the Muses, therefore his musical skills were quite impressive. Orpheus fell in love with a girl name Eurydice. When she died at a young age, it was Orpheus who decided to take the long journey to the Underworld to bring her back, so that their love could live on (if you see a pun in that there was no pun intended). When Orpheus reached the Underworld, it was his music that saved him numerous times and helped him reach Hades, whom he charmed with his lyre. Orpheus almost got his true love back, but he looked back at Eurydice which broke his deal with Hades. Orpheus lost the love of his life forever.
Eurydice- Even though her name appears in the title of the myth, Eurydice does not appear that much in the tale of Orpheus and Eurydice. She was the love interest for Orpheus. They both were married when she went for a stroll alone one day. While she was walking she stepped on a snake and died. Eurydice's soul was taken to the Underworld like all souls were when the body that they belonged to died. She was almost brought back to life, but her husband looked at her and she was taken back to Hades.
Hades- Like in all other myths, Hades is the God of the Underworld. He has two brothers, Zeus and Poseidon. He is the ruler of the dead. Orpheus pleaded to Hades to bring his wife back to life. When Hades saw his queen Prosephone's sad face as Orpheus begged to him, Hades agreed to let Eurydice go. We all know Hades as the evil god but truthfully, even though he did add the condition that Eurydice would not be able to go free if Orpheus looked back, Hades' actions were meant kindly. It is not the job of the God of the Underworld to bring us back to life, it's his job to control the dead. So for him to give someone even the chance for someone to continue their life is a huge deal and a very compassionate idea.