It's a pervasive idea: different students' brains are better suited to different styles of learning. So while one student might best comprehend a subject by hearing a lesson, another would get the most benefit from reading it on paper, and another still would learn it better by performing a task. This is a simple theory that should be easy to prove with a scientific study, but most research has shown that it's just not true.
What these studies do show is that all students benefit when a subject is taught with the appropriate style: math taught visually, for example, or language taught verbally. That's not to say all students learn the same way. Everyone varies in their strengths, interests, and previous knowledge, and research shows that it's qualities like these that have the biggest effect on how best to learn something. For example, there's evidence that beginners learn a subject best by studying examples while advanced students learn better by doing problems themselves. In the end, the idea of learning styles may even be harmful. It burdens already overworked educators, and is designed to cater to students' intellectual strengths instead of challenging their weaknesses.