Some writers use epilogues like final chapters in their books...but this is an abuse. Like prologues, epilogues are entities unto themselves. Treat them that way, and you'll end up writing them the right way.
By the time you get to the epilogue, the book is essentially over. The story should already have its own beginning and ending that takes place within the chapters of your tale. An epilogue shouldn't be tacked on at the end to bring resolution to the story -- because you should have done that already in your final scene, within the pages of the book. Epilogues are there to do something more than finish the story.
- The longer ending. If the book ends on a particularly abrupt note -- a character dies, for example -- you may wish to include an epilogue to provide a lengthier wrap-up of the aftermath. This is especially important if the end of the story doesn't provide a conclusion or follow-up. For example, what happens to the characters left behind after the death? Some epilogues may skip ahead several years to tell readers what eventually happened to the characters, or a single character, in the book.
- The continuation. If the book is part of a series, epilogues can be especially helpful. You'll want to open the door to whatever action is going to take place in the next book, and let readers know that the story is going to continue in a new installment. In this case, the epilogue should set the stage for the next book and the next part of the story.
- The style. If you write one, make sure the epilogue reflects the same style of writing as the prologue. Usually, it's best if the prologue and the epilogue both match the general tone and voice of the remainder of the book. The prologue and/or epilogue are only written in a different style or from a different POV when they're wholly separate from the rest of the story. This may happen if the story is narrated by one character, and a supporting character narrates the prologue and epilogue.