About:

Nyu's Art Meme is an artistic questionnaire made by a DeviantArtist nyu on September 25, 2007. The form asks over twelve questions about an artist.

1. Give me an introduction of yourself
2. I see. Do you have an avatar of yourself?
3. Just for fun, try drawing the same picture with your opposite hand
4. And now with your foot! :D
5. How nice! So you like to draw? What do you enjoy drawing the most?
6. Ooh… I see! What inspired you to draw first?
7. What do you have the most difficulties on in drawing? (Ex. hands, human, coloring, …)
8. Yeah, drawing ain't easy. Why don't we give it a little practice? Try drawing one thing that you see around you now.
9. Any personal tips you can give to others?
10. I have one little request… Draw me in your style~!
11. Any last comments you want to say before this meme ends?
12. Finally, you're done! Now tag 3 (or more) people!

Meme:

Typically, when something is called a meme before there is any proof of a search trend, people become discouraged in taking part, feeling that the declaration makes the meme "forced."

However, these simple "Art Questionnaire Memes" became popular with DeviantArtists for the following reasons:
The questionnaire itself is exploitable. Everyone can answer it just how they wish to. Some can skip a question, some can bend a question, and some can have a very funny answer that can inspire others to imitate it.
Overall, the form is easy to imitate. Generally, the easier it is to imitate, the more the meme will spread.

Derivatives (pics below):

Although the term "Art meme" may refer to any meme that occurs within any artform, the popularity of Nyu's Art Meme led to a number of imitators, mostly on DeviantArt, who have created so many derivatives that searches for the term "Art Meme" now return mostly derivatives inspired by Nyu's Art Meme.