Think about The Lord of the Rings. The climax of the story is when Frodo destroys the Ring, but that's hardly the end. There's a lot to wrap up after that, a lot you need to know about what the characters are doing and if any of them even survive. If the story ended right after the Ring was destroyed, the readers would have been really, really, upset. And justifiably so. Is anyone alive? What about Aragorn? What is up with Gandalf? We wouldn't know anything if the story just ended, and that would leave a foul taste in our mouths.
And so the denouement is necessary in almost all cases. It's a weird kind of thing that varies from story to story. And it's not as connected to plot as the rest of the book is. Often it is a place where the emotions of the story are resolved, or not resolved as the case may be. It is also the place where we learn that the lives of the characters will go on beyond the final page (unless that character was killed off in the climax; he's going nowhere). The future, what might be, is often the entire focus of the denouement.
This final bit of the story is also about saying goodbye. If the book did its job, you have grown to care about the characters. You love them, you hate them, you cry with them, and you're about to grieve as you say goodbye to them. A proper denouement will let you move on, finding another book to love, even as you reflect on the journey of the book you put down.
As a writer, it is your job to give all of this to your readers. You must give them a sense of completion and the knowledge that the story they were reading has truly come to an end. If you intend a sequel, you may tease it, of course, but be fair. If you're never going to write that sequel, don't leave crumbs. Leave satisfaction.