A prologue occurs at the beginning of a story.  Many prologues act as part of the exposition of the story and give background information and introduce key characters.  Prologues can occur in drama as well, and actually originated in the early Greek dramas.  A well known prologue that you might be familiar with is the one that occurs at the beginning of Romeo and Juliet; in this particular prologue, Shakespeare uses the chorus to introduce the setting, Verona, the idea of feuding families, and the theme of "star-cross'd lovers" (6).

The key difference between a prologue and a synopsis is that a prologue actually functions as part of the story, and a synopsis is a condensed, summarized version of the story.  Think of a synopsis as bullet points for all the most important moments and characters in a story.  A well-done synopsis can give you an overview of a written work and present the most important main ideas.