'I have an outstanding trait in my character'- what is Anne reffering to?explain in content

In order to understand this quote, you have to look at it in its entirety. Anne sees her outstanding trait as 'knowledge of self,' the ability to see herself and her actions without prejudice. This doesn't mean she sees herself as perfect, but rather that she has a full awareness of her own faults. Most teenagers have this ability and refuse to use it; many adults do the same.

Anne's final analysis is dead on; parents can only give their children guidance and advice. After that.... it's up to the children to take their parent's lessons to heart.

“I have one outstanding trait in my character, which must strike anyone who knows me for any length of time, and that is my knowledge of myself. I can watch myself and my actions, just like an outsider. The Anne of every day I can face entirely without prejudice, without making excuses for her, and watch what's good and what's bad about her. This 'self-consciousness' haunts me, and every time I open my mouth I know as soon as I've spoken whether 'that ought to have been different' or 'that was right as it was.' There are so many things about myself that I condemn; I couldn't begin to name them all. I understand more and more how true Daddy's words were when he said: 'All children must look after their own upbringing.' Parents can only give good advice or put them on the right paths, but the final forming of a person's character lies in their own hands.”