Yui

is a mysterious girl found by Kirito and Asuna around the forests of the Floria, the 22nd Floor of the Floating Castle Aincrad.

Her official name is «Yui-MHCP001».

Morning Dew Girl (Aincrad 22nd Floor, October 2024)
Hearing a rumor about a "ghost" that has appeared on the forests around the 22nd floor, Kirito and Asuna decide to check it out themselves. There they meet a young girl who suddenly falls unconscious. They immediately take her back with them and are faced with several concerns about her after finding out that she's not an NPC or part of some random quest. Along with this, she doesn't have a cursor and is far too young to be a normal player as there was an age restriction while setting up the NerveGear at signup, forbidding children below thirteen. Later, during a quest to find the «Army's» leader, Thinker in the dungeon of the «Black Iron Castle», Yui touches a stone left around and immediately regains all her memories. Yui, now knowing her purpose as an AI who will be erased now that the game recognizes her as an alien object, expresses her gratitude to Kirito and Asuna for taking care of her. Just as she disappears, Kirito uses his computer skills to retrieve her and store her heart as a tear crystal.

ALfheim Online
After SAO, Kirito unknowingly transfers his SAO data to ALO. Most of his data is deemed unusable and corrupt, but he manages to retrieve Yui from his item window. Here, she is converted into a navigation pixie, and she leads Kirito to the proper locations throughout the land. Yui also finds information stored within the game's databases to help find her mother, Asuna. She is able to return to her regular body, but only does so when alone with Kirito and Asuna.

With Yui's help Kirito was eventually able to unite and rescue Asuna from Sugou Nobuyuki. When they met Asuna again, Yui returned to her regular body, and they shared a "family hug." Unfortunately before they could escape, Sugou intervened and attempted to delete Yui, but she managed to escape to Kirito and Asuna's relief. Yui attempted to reunite with Asuna and Kirito afterwards, but she was only able to after Kirito successful destroyed Sugou's avatar and helped Asuna log out of the game.

While Yui was sad that Asuna had already left, she understood why Asuna had to return to the real world. Kirito promised Yui that both he and Asuna would visit her soon. Before Kirito left to meet Asuna in the real world, Yui informed Kirito of the "seed" that had been given to him as well courtesy of Kayaba Akihiko. Yui informed Kirito that regardless of what happens to ALO, she will be fine because she exists in Kirito's Nerve Gear.

Sometime later, Yui joined Kirito, Asuna, and their friends on a new adventure in ALO.

Gun Gale Online
Prior to Kirito entering GGO, she is mentioned in a conversation between Asuna and Kirito about the possibility of her having a "younger sister" in the future and how great it would be if she would be able to  Yui, crossover into the real world.

Through Asuna's cell phone, connects the Bullet of Bullets tournament to the heart beat monitor, letting Asuna and Nurse Aki to see what is currently happening. Seeing that Kirito is losing the fight with his opponent, Yui tells Asuna to hold his hand, which helps Kirito remember of the gun that was still in the holster at his side.

Project Alicization
After Kirito is critically injured by former Laughing Coffin member Johnny Black and subsquently kidnapped by Kikuoka Seijirou, Asuna and her friends began to think there was no hope in locating Kirito. However, Yui convinced her mother not to give up just like Kirito refused to give up finding Asuna when she was trapped by Sugou. It was enough to restore Asuna's resolve and with Yui's help along with Koujirou Rinko (the deceased Kayaba Akihiko's lover) Asuna was eventually successful in finding Kirito.

Hardware
Yui is the first version of the «Mental Health - Counselling Program» of «Sword Art Online». She is a «Top-down AI» made to monitor the mental health of the players of SAO. She's a pseudo artificial intelligence built from a program atop an existing computer architecture. Top-down AIs can be considered as a cluster of binary. She later gains access to the real world through a VR probe designed and created by Kirito.

Trivia

 * Yui looks like Sachi. Many fans notice this too, but some take this as a coincidence only.