Fluffy Ponys are a fictional species of animals, similar to My Little Pony - Friendship is Magic ponies. They are commonly portrayed as being around the size of a bunny rabbit and are known for being very cute, and very stupid.
They are bred for maximum cuteness, and have the ability to talk, however, due to being bred for cuteness they have functional skills equivalent to a toddler.
Commonly stories about them are posted on 4chan's /mlp/ board. Stories range from protagonists beating and abusing fluffy ponies, or having cutesy experiences with them. They also love spaghetti and hugs.
There is also a lot of fan art of them.
All of this and more can be found on the My Little Pony fan art wikipedia page.