It could mean that the boy removed or wiped out a story. Maybe he erased a written story, like from a piece of paper, or perhaps he's trying to forget or hide a story that he knows.
The phrase 'the boy erased story' might imply that the boy has taken some action to eliminate a story. This could be a story he was writing and decided to get rid of, or it could be a more metaphorical story, like an event or memory that he doesn't want to be associated with anymore. For example, if he was involved in an embarrassing incident and he wants to 'erase' the story of it so that others won't know.
Well, 'the boy erased story' is rather ambiguous. If we take it literally, it might refer to a boy using an eraser to remove a written story. However, in a more figurative sense, it could mean that the boy is trying to obliterate a narrative. It could be a story he's heard that he doesn't like and is mentally trying to erase it from his mind. Or it could be his own story that he wants to rewrite by erasing the original version, like if he made some mistakes in the first telling and wants to start anew.