The American Heritage® Dictionary of the English Language defines the word "meme" like so
n. A unit of cultural information, such as a cultural practice or idea, that is transmitted verbally or by repeated action from one mind to another.
The word apparently finds its origins in the same sorts of places as the words "mimic" and "mime" (meaning "to copy; to imitate"). But I couldn't help but notice that it looks like "me me" without the intervening space. "me me" … two "me's" … "me too!" (sometimes represented as <aol/>). When it comes to Internet memes, I suspect my bogus etymology of the word reveals more about the motives behind these information transmissions than the Greek can offer.