Parallel events are similar events that occur more than once in a story. Normally, an event takes place or a character reveals something about himself that foreshadows an occurrence that is important to the story later.
An example of using parallel events in literature is in "Of Mice and Men." The character Lenny confesses to George that he accidentally killed mice when trying to pet them. Steinbeck uses this revelation as an indicator of tragic events that take place later in the book. This literary device is one of many that are used by writers to hint at things yet to come.