To imply about something in literature is to have a speaker or a character commit an action that conveys a message for the reader to pick up out of the text without it being directly stated.
In the short story by Steinbeck "Of Mice and Men" there are two men who travel together looking for work. One is George, who is intelligent and small in frame. Lenny, the other, is a large man who is simple minded. George looks after Lenny. They get a job at a ranch and they meet Candy. Candy is a washed up ranch hand who is not much good to anybody. He has an old dog that is the same way. The men decide that the dog needs to be put down. They take it outside and shoot it. The words do not directly state that the dog's situation is similar to Candy's.
Another instance of implication in the story is the way Lenny is always petting things too roughly. He keeps a soft dead mouse in his pocket that he has accidentally killed. Lenny and George have a dream to have a ranch together. Lenny wants to raise rabbits on the ranch because they are soft. It is not stated but it is implied that Lenny would be too rough with the rabbits if he were to have his dream fulfilled. The reality of this becomes evident when he accidentally kills the puppy.
After Lenny had accidentally killed Curley’s wife, George is afraid for Curley to catch up with Lenny. No one knows for sure that Curley would torture and make Lenny experience a terrible death in retaliation, but George just knows it. George shoots Lenny to protect him from such a fate.