Ai-chan's name comes in part from Ai-chan's real name. Just as Ai means love, Ai-chan's real name also contains the word love. Specifically, Ai-chan's real name means "A love to be hold".
As for the avatar, it's just Ai-chan reminiscing about the good old days of school, where Ai-chan changed clothes together with the other girls, discuss about whose bras were the cutest and groping each other in gym class. And also lamenting about not making a move on my really hot and gorgeous senior back in school for fear of being turned down, who turned out to be a hardcore lesbian. After all, this avatar was chosen back in January.