Most grammar gods and goddesses agree that the occasional fragment is okay if it serves a purpose. In creative writing, such as narrative or descriptive essays, fragments can be deployed on purpose in order to create a whole host of effects: emphasis, momentum, mood, and so on.
In fact, you may have noticed that Shmoop uses fragments from time to time. Because we do. See? That last sentence was a fragment. That's because we're communicating to you in an informal tone. It's a style choice. And Shmoop is nothing if not stylish… with the hand-embroidered Snuggies to prove it.
Having said that, we'll guess that your teachers and future professors are going to expect you to write in a much more formal tone for most of your academic papers, so you should learn to recognize fragments when you see them—and you should avoid producing them.
Save those artful fragments for your first novel, and make sure you scowl broodingly in your author photo. (Or wear your coolest white suit, loudly patterned shirt, and giant pocket square.)