dzzthink: Yui comes to save Shinji, bringing him out of the despair Leliel has cast him in. As in the Bible: 'the light shines in the darkness, and the darkness has not overcome it.' John 1:5
Dr. Nick: Yui wasn't this long-haired at the time when she was absorbed into the core, so I guess she likes this look. Perhaps this connects to Unit-01 itself sporting long hair in EoE while floating in space.