This covers Moonbeam's appearance in The Festival of Lights specifically. Her color palette also differs here slightly. See here for her debut in The Curse of the Statuettes

Moonbeam is a Unicorn mare. She is about the same age as the
Mane Six. As a filly, she spent almost all of her time studying and
practicing magic, and her only friends were her many dolls and
figurines. She never properly learned how to make pony friends
(sound familiar?). Unlike Twilight Sparkle, she shied away from
every opportunity to meet new ponies or experience new things.

She was often overlooked by most ponies around her and eventually, feeling as though she would never
fit in, she left her home to travel Equestria alone. Without friends to keep her company, she became
more and more withdrawn and isolated. Eventually she was drawn to the Badlands after detecting a
strange magical presence there.

With the end of The Curse of the Statuettes, Moonbeam has learned a lot about herself and the
meaning of friendship. Where before she was driven by isolation, misunderstanding, and loneliness, she
now just wants to be understood and make friends. She is still struggling, but with some help she can
certainly turn herself around.

Roleplaying Moonbeam: Moonbeam is very apologetic for the trouble she caused in the last adventure
(see The Curse of the Statuettes) and wants nothing more than to make up for her past mistakes.
Although she has learned that real ponies make truer friends than statuettes, she is still very shy and will
prefer to let anypony else take control of a social situation.