There appear to be three Mr. Radleys in the novel.
The text tells us that the Radley Place is three doors south of the Finch home. At the beginning of the story, we discover that Dill, Scout, and Jem have been trying to get Boo Radley out of the house. The children are mostly curious about this "unknown entity" in Maycomb; rumors are that he is some "malevolent phantom" who is responsible for all the petty crime in Maycomb.
We also learn that Mr. and Mrs. Radley live at the Radley Place with their two sons. The younger of the sons is Boo (Arthur), and the elder is Nathan. It is said that no one knows how Old Mr. Radley (the first Mr. Radley) makes his living. He is described as a "thin leathery man" with colorless eyes, sharp cheekbones, and a wide mouth. His posture is always said to be "ramrod straight," and he never speaks to the children.
Legend has it that Arthur or Boo (the youngest Mr. Radley) was once caught taking up with a gang of boys from Old Sarum. Boo evidently engaged in juvenile mischief and was caught when his gang locked Mr. Conner (Maycomb's beadle) in the courthouse outhouse.
The judge sent the boys to an industrial school, but Old Mr. Radley felt that it was a disgrace for his son to attend. He convinced the judge to release Arthur into his care and promised that the town would have no further trouble from the young scapegrace (rascal). At this point, the text tells us that Arthur (Boo) was not seen again for fifteen years. When he was heard from eventually, Arthur set tongues wagging in Maycomb. He was said to have stabbed his father in the leg with a pair of scissors. So, the general consensus was that, at thirty-three years old, Arthur needed to be incarcerated in an asylum for his own good.
Again, Old Mr. Radley convinced the authorities to release Arthur into his care. This is how Arthur eventually comes to be known as Boo; because he is never seen in public again after this point, all sorts of sordid stories emerge to explain his absence. As time passes, Old Mr. Radley dies, and his presence at the Radley place is taken over by Nathan Radley (Boo's older brother). Essentially, Nathan comes up from Pensacola to become the new Mr. Radley. He is far friendlier than his father had ever been, but he still keeps Boo locked up in the house.
As rumors continue to abound about Boo, the younger Mr. Radley eventually comes to take on a frightful persona in the community's eyes. Jem swears that Boo is at least six-and-a-half feet tall; eats squirrels and cats for his meals; wears a jagged scar across his face; has yellowed, rotten teeth; wears a bug-eyed expression; and drools uncontrollably much of the time. This is the main reason the children create all sorts of diversions to draw Boo out of his house. They want to see if reality matches everything they have imagined about Boo.
Although Boo proves elusive, it is evident from the story that he harbors great affection for the children. At one point, he leaves gifts for Scout and Jem in the knothole of an oak tree on the Radley property. Most significantly, it is Boo who later saves the children from certain death at the hands of Bob Ewell after the Halloween pageant.