Yotsuba Koiwai is a the main character from the manga series Yotsuba&!, previously featured on the one shot Try! Try! Try!, by Kiyohiko Azuma. Over time, Yotsuba was adopted by 4chan as the site official mascot, appearing in banned users messages, ads, logos, and HTTP 404 messages, leading to the nickname of 404 Girl.
Yotsuba Koiwai is the main character from the comedy manga Yotsuba&!. The manga follows his daily adventures as she learns about the world around her, guided by her father, the neighbors, and their friends.
Adopted by 4Chan
"Yotsuba Channel" is also 4chan's name in Japanese. Due to this similarity in names, 4chan adopted the character Yotsuba Koiwai as their official mascot. Images of Yotsuba began appearing (and to this day appear) whenever a member is banned, a file is not found (also leading her to be called 404 girl), and for a time appearing on numerous banners and webcomics around the website.
She started being referred to as 404 Girl when an Anonymous asked for Rule 34 for the 404 Girl. This rule 34 was instantly considered taboo, and thus many trolls have since repeated the request.
Yotsuba's innocence is one thing Anonymous will not touch; in a way, she is like Anonymous' little sister. Usually, attempts at things such as Rule 34's on Yotsuba will lead to extreme amounts of harassment, flaming, and even a ban.
Saying that she merely appears on things such as image macros and videos is an understatement; she is actually woven into the the history of 4chan, as the software that 4chan runs on was lovingly code-named "Yotsuba."