Auditory learners learn best by hearing. These are the kids who do well with programs where there is a lot of reading out loud, explanation, etc. They will often repeat back what they hear. My own guess would be that they probably talk a lot, too, as talking about what they learn helps them remember it. I have a son who, as a friend points out regularly, could talk the paint off of a wall, and I think that he will, when he matures a bit more, be an auditory learner.
Visual learners learn best by seeing.
They read something in a book and can remember which page it was on, and where on that page it was. I have heard that these are the kids who do well with textbooks and worksheets, but have not had any personal experience with this kind of learner yet. Most young children are kinesthetic, because developmentally they are not mature enough to be anything else. Their attention spans aren't long enough and their visual and perceptual skills are not developed enough. As they mature, their learning style will become more evident.