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.

Powers and abilities
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, as well as, in Princess Luna's absence, the Moon as well. She likely has many other powers which have not been revealed.

One Thousand Years Ago
A millennium ago, the day/night cycle of Equestira was ruled by two sisters: Luna, the younger, who brought the night, and Celestia, who brought the day. The ponies of Equestria all enjoyed and loved Celestia's daylight, but were all asleep at night, causing Luna to grow jealous of Celestia's day and become Nightmare Moon, vowing to plunge the world into eternal darkness. Celestia with great sadness and regret, stopped her using the Elements of Harmony, and imprisoned Nightmare Moon within the moon.

Modern Day
A thousand years passed peacefully under Celestia's rule, until the Summer Sun Festival was held in Ponyville. Shortly beforehand her student Twilight Sparkle informed her of the return of Nightmare Moon, to which Princess Celestia responded by sending her to gain the friends she'd need to activate the Elements of Harmony. Nightmare Moon escaped as the signs indicated, capturing Celestia and appearing in place of her at the festival. When she was freed by Twilight Sparkle and her friends and Nightmare Moon was transformed back into her Luna form, she forgave her sister, and explained they should rule together.

With Equesatria back to normal, Celestia allowed her student to stay in Ponyville with her friends, giving her a "mission" to study the fundamentals of friendship.

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 Equestira is a principality.