The Phoenix Eye is an amber crystal with wings in its setting. It is said to be the Eye of the Phoenix because its eye burns with the fire that consumes the life force of anyone that comes in contact with it (The Eye of the Phoenix).
Morgause gave Morgana a Phoenix Eye to give to Arthur on his quest to gain the trident of The Fisher King so it
An illustration of the Eye.
would kill him. Morgana was told to make a likeness of Arthur and bind it to the gift using the skills that Morgause taught her. In her chambers, Morgana created a doll with pieces of wood and cloths. She then burnt the poppet on a candle and she lighted the "gift", which appeared to be some kind of ashes in a metal box (perhaps even ashes of a phoenix itself) with her magic. This caused the Eye to light and to start consuming
Arthur's life force. Morgana was forced to repeat this ritual twice because she was interrupted by her maid Gwen. When Morgana repeated the ritual, it worsened the Eye's effect on Arthur. The Eye weakened Arthur across the journey but he was able to hold on and make in to the Fisher King's tower. Merlin and Gwaine followed Arthur and Merlin was able to take the Phoenix Eye off Arthur before it killed him. He then gave it to the Fisher King to grant his wish to die as he was kept alive for years after a fatal injury (The Eye of the Phoenix).
Although not confirmed or shown, it is also possible that a Phoenix Eye can also cloud the mind of its victim and weaken their awareness because Arthur, while wearing the bracelet, was unaware that he was being weakened and did not suspect the Eye's danger.