The "shiny clean line" that "stood out on the dull wire" was the mark left by the knife wielded by Bob Ewell. It is significant because it proves that Ewell meant to kill Scout; her life was saved when the wire on her costume deflected the sharp thrust of his weapon. Bob Ewell was drunk, and Mr. Tate observes that he "meant business", noting ironically that he had "enough liquor in him to make him brave enough to kill children" (Chapter 29).
In the aftermath of Bob Ewell's attack on the children, Tate and Atticus have a chat. Tate helps Atticus to see that they should not bring Boo Radley into the picture. He is a recluse and all the public attention would not be good for him.
Tate asks Atticus to show him Scout's costume. When he examines the costume, it becomes clear that Bob really meant to kill Scout and Jem. The shiny-clean line was made by his knife.
To Kill A Mockingbird:
Atticus fetched the remains of my costume. Mr. Tate turned it over and bent it around to get an idea of its former shape. “This thing probably saved her life,” he said. “Look.”
He pointed with a long forefinger. A shiny clean line stood out on the dull wire. “Bob Ewell meant business,” Mr. Tate muttered.
“He was out of his mind,” said Atticus.
“Don’t like to contradict you, Mr. Finch—wasn’t crazy, mean as hell. Low-down skunk with enough liquor in him to make him brave enough to kill children. He’d never have met you face to face.”
In a state of drunkenness, Bob Ewell did what was unthinkable. Atticus, therefore, realizes the extent of human depravity.