Princess Celestia

Princess Celestia is a pegasus unicorn pony with white color, a flowing mane of rainbow color, and a sun cutie mark. She is the older sister of Princess Luna, and mentor of Twilight Sparkle, referring to her as "My Faithful Student".

Personality
Princess Celestia is a wise and kind pony. As a teacher, she often does not directly state her goals, but rather gives the advice to help her students find the answers they need. Though viewed with great reverence and fear due to her position she often encourages her subjects to relax with jokes and gentle questions, and shows great patience with any rudeness towards her.

As seen in A Bird in the Hoof, she can be a bit of a prankster in her own subtle way, tricking the Cake family into overfilling her cup.

Skills
Being one of the two Pegasus Unicorn Ponies, Princess Celestia possess magic far beyond normal unicorn ponies. She is able to control the sun and the daytime sky, bringing them out each day and then moving them away to make room for the night. In Princess Luna's absence, she was responsible for moving the Moon, as well. She likely has many other powers which have not been revealed, and is either immortal or extraordinarily long-lived.

One thousand years ago
The legend narrated in the first episode tells that one thousand years ago, the day and night cycle of Equestria was ruled by two sisters: Luna, the younger, who brought the night, and Celestia, who brought the day. However, Luna grew jealous of her sister: the ponies of Equestria all enjoyed and loved Celestia's daylight, but were all asleep at night. No one was awake to appreciate the beautiful night she had worked so hard to create. Eventually, this jealousy and bitterness drove Luna to become Nightmare Moon, and prevent Celestia from bringing forth the sun. She intended to keep Equestria in eternal night. Her older sister, with great sadness and regret, stopped Nightmare Moon by using the Elements of Harmony, and imprisoned her within the moon. Henceforth she became known as the Mare in the Moon and knowledge of her slowly drifted to the area of myths.

Nightmare Moon's escape
A thousand years passed under Celestia's rule, until the night of the Summer Sun celebration, held in honor of Princess Celestia and the longest day in Equestria. Shortly before the celebration, Celestia's student, Twilight Sparkle informed her of the imminent return of Nightmare Moon. Celestia responded by sending Twilight to Ponyville to oversee an upcoming party, and make some friends. The princess knew Twilight had the power to stop Nightmare Moon, but the young unicorn needed to understand friendship in order to wield the Elements of Harmony. Nightmare Moon escaped as prophesied, and appeared in place of Celestia at the celebration.

After Nightmare Moon was transformed back to her former self, Celestia offered forgiveness to her little sister, and explained they should rule together. With Equestria back under both sisters' rule, Celestia allowed her student to stay in Ponyville with her friends, instructing her to study the "magic of friendship".

Present day
Celestia remains the co-ruler of Equestria, alongside Luna. She is often seen attending major events or functions, such as the Running of the Leaves and the Best Young Flyers Competition.

She has instructed Twilight to send her periodic reports on the magic of friendship in the form of letters, which Twilight sends via Spike. These letters typically serve to illustrate each episode's moral for the show's viewers.

However, in several cases, Celestia has been present during an episode, and Twilight delivers the report to her in person. Examples include "Swarm of the Century" and "Fall Weather Friends." In "Sonic Rainboom," Rarity delivers the report instead.

Celestia makes a surprise cameo at the end of "Feeling Pinkie Keen," dropping out of the sky to grab Spike's letter and then taking off just as quickly, confirming another one of Pinkie's "Tail Twitch" predictions.

Trivia

 * Princess Celestia was originally supposed to be Queen Celestia, as is logical considering her position, but Hasbro requested the name be changed as Disney has caused princesses to be associated with good and queens associated with evil. At best, we can assume that Equestria is a principality. Lauren Faust has confirmed that Celestia is the highest authority - there is no "king" or "queen" to speak of.
 * Her name comes from Latin "caelum" meaning "sky" or "heaven". By analogy to her sister we might speculate that her original name was Sol.
 * Rarity's fantasies reveal that Celestia is supposed to have a "nephew". While many doubted his existence (the only logical choice of a mother is Luna and it's hard to hook up with anyone during a thousand years long imprisonment in the moon), Lauren Faust described him as real pony and (about) 52nd great grand nephew on mother's side. Considering the fact that Lauren haven't yet decided if the Sisters has parents or not, it could be just a joke or irrelevant information.
 * Despite appearing white in the show, every toy release of Princess Celestia has been pink in color. A possible reason is that the retailers requested it in order to appeal to little girls.
 * During the show, Celestia was never referred to as a "goddess". Lauren never used this word as well.

Appearances
Princess Celestia first appeared in the book Twilight was reading at the beginning of "Friendship is Magic, part 1". She made a full appearance in the next episode. Since then, she is sometimes shown reading Twilight's letters and during occasional visits.