A sentence is defined as a group of words containing a subject, a verb, and a complete thought. If any of these elements is missing, then the group of words isn't a sentence. A fragment is a group of words that is punctuated like a sentence and that is trying to function as a sentence, but one of the necessary elements is missing.
There are several ways to find and correct fragments. Any group of words functioning as a sentence should be checked for the basics. Does it have a subject? Does it have a verb? Does it start with a subordinating conjunction or a relative pronoun that keeps the thought from being complete? If the answer to any of the questions is no, it is a fragment.
Correcting fragments is fairly simple and you have several options. For a fragment that is missing a subject or verb, add the missing element. If the problem is a subordinating conjunction, the conjunction can be removed which would make the fragment a complete sentence. Another option is to join the fragment to another sentence either before it or after it in the paragraph creating a complex sentence.
No matter how you choose to correct the fragment, it is important for you to eliminate them from your writing. Fragments are considered to be a major grammatical error in writing because they indicate that the writer isn't sure what a sentence is. Readers will often not pay attention to the point a writer is making if the reader thinks the writer doesn't even understand how to write a complete sentence.