Fluttershy is one of the main 6 ponies in My Little Pony: Friendship is Magic. She is the element of Kindness in show. Fluttershy, as her name suggests, shies away from most other ponies, being more comfortable around other animals. Because of this, she finds herself fairly capable of talking with most Anonymouses, but often takes it a bit too far. Fluttershy is the only pony capable of using 'The Stare,' which allows her to make demands of other beings, bending them to her will.
Fluttershy is the first pony to be written of in Pre-AiE threads, brought about in part by an unrelated artist TheWeaver's comics. The comics depict Fluttershy trying (and failing) to seduce Anonymous and get him to have sex with her. The stories gained popularly especially because of the paradox that the 'kind and shy' pony would be so keen on having sex. A plurality of hetero male MLP fans appear to regard Fluttershy as the most physically attractive pony, and so you see the comedy potential here of stories in which Anonymous doesn't want to bone the pone.
The original Fluttershy, which is still commonly used, is Flutterrapist. She wishes to have sex with Anonymous, using various and often convoluted plans to seduce him or otherwise force him to have sex. Authors generally have her fail horribly because it's funnier that way.
An offshoot of Flutterrapist, Fetishshy still wishes to have sex with Anonymous, but instead of trying to force him into compromising situations, instead attempts to guess what Anonymous's secret fetish is, in order to make him fall for her. Like Flutterrapist, Fluttershy usually fails to get Anonymous, and there is considerable overlap between "Flutterrape" and "Fetishy" stories. The failure is in fact played for comedy. Sex isn't usually funny. Trying to have sex and failing, on the other hand, is comedy gold.