The phoenix is a mythical bird who rises from its own ashes every time it dies giving it immortality. It is usually associated with the sun and fire. In most myths it dies in a blaze of fire, though there are some myths where it doesn’t. In Medieval Europe the phoenix was a symbol of royalty and even called “the royal bird” due to the purple hue it had back then. Now in the west the phoenix is usually depicted with feathers that are red, yellow, and/or orange which give it a more fire-like appearance. Throughout history the phoenix has symbolized the sun, time, the longevity of the Roman Empire, metempsychosis (transmigration and resurrection of the soul, resurrection, life in a heavenly paradise, and multiple aspects of Christianity.
The first myths of this bird come from Greece, though there are some earlier myths with a similar bird called the Bennu in Ancient Egypt. There are similar myths all over the world. In China, the Fenghuang is the ruler of all birds, is not associated with fire, and is typically seen as female. In Japan the Fenghuang is called Ho-o. If you are going to be writing something using a phoenix as a symbol keep in mind that the myth changes slightly depending on your setting and where your characters come from.