"It's a shame you had to see him on a Burning Day ...He's really very handsome most of the time..."
-- Dumbledore to Harry (CS12)
Burning Day is the day on which a phoenix bursts into flames and is reborn from the ashes (CS12).
When Harry saw Fawkes the phoenix on a Burning Day, his eyes were "dull" and he seemed ill, resembling a "half-plucked turkey" with tail feathers falling out. Also, the large bird was making a gagging sound that made Harry think he was dying. Just then he burst into flames resembling a "fireball." A few minutes later, an ugly baby phoenix was reborn from the ashes.