I had never actually spent a lot of time thinking about that phrase (the insignifiacant girl; A phrase from the song "Cyborg Mermaid" of the Battle Angel soundtrack) or spent time trying to understand its significance towards the character that it was created for. However, that didn't keep me from trying.
In the first book, a gathering Doc Ido stumbles upon the head of our heroine Gally, resting on a pile of discarded rubble of the "Scrap yard." Without hesitaion, Ido collected what remained of her to be once rebuilt in his lab. From there, Ido rehabilitates Gally and awakens her from her long and empty dream. It was at that moment, the moment she first opened her eyes and saw Ido, that a long, impressionable, and spiritual relationship had begun.
Ido was the key factor in Gallys' life and growth. Despite her massive strength and agility, she always looked towards Ido for security. However, Ido always looked to Gally as the only innocence to walk Scrap Yard, I was for that reason that Ido first objected Gallys' descision to become a hunter warrior.
Once Ido accepted Gallys' chioce, He became more curious of her past and of what she would obtain from her career as a hunter. It was then that Ido was afraid, but curious of the course that Gally was taking, and encouraged her full heartily
So what significance is this to the "insignificant" girl? Perhaps I'm looking to deep into this, but I always saw Ido as the life preserver in Gallys' ocean of affairs. Later in the series once she had finally felt complete and safe, Ido was murdered and taken away from her. She was powerless towards protecting him and despite all that they had been through, she was once agian alone to the white that flooded her mind and fueled her hatred. What significance did there time together have. What significance did her life, protecting those she felt were sacred to her bring when all they did was take away from her or leave her alone. Even her encounter with Zapan in the berserker body, the people of the town came to a raging riot ready to sacrifice what they thought would be the answere, Gally. However it was even before all this that she had been tainted by reality for the first time, when they took away her love,Yugo.
Yugo was a young self employed indevidual that occasionally aided Ido and performed a few under the table jobs along with it(Spine theft). However, always unaware that he had captured the eye of now reborn and impressionable Gally.
When Gally first encountered Yugo, she was immediately attracted to his view on life, one that she had never seen due to the unsavory surroundings of the Scrap Yard. Despite that she was mostly constructed of metal, her emotions and how she responded to them was completly human. Yugo managed to ignite a passion that she was not yet aware of which is cause for anyone to be attracted to .