If you don’t know who this is, here’s a video compilation of some popular gifs that are related to one of her sub-memes, the Osaka Shoe Kick:
Her real name is Ayumu Kasuga. I have a feeling that she should be a parent meme of her own because she seems to have influenced several memes, one of them being the Shoe Kick. Even some people questioned her memecity on this site. You can find the short discussion here: http://knowyourmeme.com/forums/1-general/topics/198-azumanga-daioh
In ED, she is the only character out of all the characters in Azumanga Daioh to have her own article written about her: http://encyclopediadramatica.com/Osaka
Wikipedia states the she is the most notable of the most influential anime heroines due to her differentiation from the stereotypical female anime character: http://en.wikipedia.org/wiki/Ayumu_Kasuga
Here’s a Macrochan link for existing images and gifs that are related to Azumanga Daioh as a whole: http://macrochan.org/search.php?tags=Azumanga+Daioh
And here’s a YTMND Wiki link for her: http://wiki.ytmnd.com/Osaka
So, what do you guys think? Note that I just breezed through this and I haven’t done enough research about her to know what some of her other sub-memes are like.