As any good journalist will tell you, it's best to let your sources tell the story. That's true of fiction or news writing, and it's done with quotes.
For one thing, the use of quotes varies the voice of the story. What do I mean by voice? Every writer has a voice, a certain tone to his writing. That's a good thing. Every writer's voice is different, so it gives variety to the world of literature. At the same time, big chunks of narrative in the writer's voice can bog down your writing. Almost all writers (including me) are in love with our own voice, but it can get very boring for the reader. That's why it's a good idea to break it up by letting someone else do the talking.
It's easiest to add quotes to news writing. You've interviewed a variety of sources (I hope, otherwise you need a different article), so now all you have to do is pick the quotes that best tell your story. As you get more experienced with news writing, you'll learn to weave them into the story or, even better, structure your story around them. If you're not at that point yet, a good rule of thumb is to place a quote every few paragraphs.
It's a little more difficult to add quotes to fiction, not because it's hard to make up things for your characters to say, but because it's a challenge to make sure those quotes aren't also in your own voice. If every character sounds the same, it makes your situation worse, not better. On the other hand, if your characters are too overdone, the dialogue become laughable-so you can see how tricky quotes in fiction can be. Still, if you achieve the right balance, it takes you work to the next level, making it worth every bit of the work you put into it.
Two more notes on quotes: When writing nonfiction, quotes give an extra note of authority to your writing, especially when the source is credible. Also, no matter what genre, quotes generally add white space to the page. I'll tell you a secret…readers love white space. It makes them think they have less work to do to get through a page, so they're more likely to keep reading-and that's good for you!