Why did Arthur Radley save the kids? How did he know the children were in danger?

Boo watched out for the children, even though they'd never seen him, that didn't mean that he hadn't seen them. He left them gifts, sewed Jem's pants, and even laughed at them. He was their friend..... a friend from afar. We don't know exactly what signaled the danger Bob Ewell posed that evening..... possibly Boo saw the children walking alone..... maybe he heard a cry. None-the-less, he was there when they needed him.