We can see examples of self-fulfilling prophecies in literature and everyday life, and an example might be if you become so nervous before a presentation that you do poorly. If you become so nervous that you are sweating a lot, have trembling hands that make it hard to read your notes, and stammer over your words, this would be an example of a self-fulfilling prophecy: you think your presentation will go badly, and because you are thinking this, your nervous behaviors cause the presentation to be unsuccessful.
Or, maybe you had a crush on someone, but a friend said your crush would never go out with you. After hearing this, you never ask your crush on a date, therefore never going out together. If you had not listened to the "prophecy," or the words of your friend, you might have simply asked the crush on a date, and who knows what might have happened instead.
One of the most famous examples of a self-fulfilling prophecy in literature can be found in Shakespeare's Macbeth. While our real-life examples of a "prophecy" might be things other people tell us in passing or ideas we impose on ourselves, in this play, three witches tell Macbeth a number of real prophecies. They tell him he will be king, and when he shares this with his wife, she convinces him that they should kill Duncan. Macbeth does so, and therefore takes the crown.
If Macbeth had never heard the prophecy, he would not have taken the actions of murdering Duncan, so the prophecy was self-fulfilling. Unsatisfied, Macbeth seeks out the witches again for more information. The new prophecies they offer tell him to beware Macduff, so Macbeth has Macduff's castle attacked. This encourages Macduff to seek revenge and motivates him to strike the blow against Macbeth himself. Macbeth thus fulfills the prophecy himself by killing Macduff's family—if he did not, Macduff might not be as motivated to fight against Macbeth.