Celestia is a radiant white (perhaps very light pink) winged unicorn, sometimes known as an alicorn or any of a number of other silly terms, with a floating prismatic mane and tail that seem to constantly defy gravity.
To play Celestia, one must certainly be able to maintain a calm proud leader persona, but this is primarily her public image. However she behaves in personal visits (e.g. towards Luna, Discord, and Twilight) is more or less entirely up to the player.
The RP (Just Draco, signed Derphoves 22:28, December 17, 2011 (UTC)) is generally of the persuasion that Celestia is extremely busty, due partially to the exaggerated blinding beauty of the sun, in contrast to Luna's relatively petite stature due to the moon's more modest beauty.