Fragments are incomplete sentences that lack either a subject or a verb, making them unable to stand alone as complete thoughts. They often occur in writing when a thought is not fully expressed, leading to confusion for the reader. For example, "Running through the park" is a fragment because it does not tell us who is running. In writing, fragments can be used intentionally for stylistic purposes, such as creating emphasis or conveying a character's thoughts in literature. However, in formal writing, it is generally important to avoid fragments to ensure clarity and coherence. Proper sentence structure helps convey ideas effectively.