"a high level of character" -> It's hard to explain it in one short sentence for me. So, allow me to describe it I think it means more than one thing, when it comes to making decisions it's good when you are a steady or level-headed person (down-to-earth). You can distinguish yourself, but that doesn't necessarly mean anything negative.
I also dear to look at it as; that you live with good intentions.
- For Teachers