How does Walter claim he almost died his first year of school?
There is a pecan tree in the Radley yard. The Radley property backs up to the school. Walter Cunningham tells Scout and Jem a story about his first year attending school. During that time, he ate some of the Radley pecans and it is implied that they had made him sick. He says he nearly died. Walter claims that Boo Radley poisoned the pecans "and put 'em over on the school side of the fence" (To Kill a Mockingbird, Chapter 3).
Walter's story of supposedly poisoned pecans is just one of the many rumors involving Boo Radley. These rumors usually make Boo out to be a monster. Such stories claim that he is violent and wants to cause harm to others. Walter Cunningham's story about Boo confirms their already negative opinions. Scout and Jem are already terrified of Boo and the Radley property when Walter tells his story to them.