I actually was a Kinesiology major and am familiar with the field. As an Athletic Training major you can do athletic training for a career at various places and levels. Athletic trainers can work for schools such as colleges and universities, but they can also work at various healthcare facilities. With this route, not only will you need a degree but also certification through the National Athletic Trainer's Association.
There is also the option for graduate school with this degree and concentration. You could go on to get your Master's in Athletic Training, or perhaps get your doctorate. This major and concentration would relate to many different occupations such as a physical therapist, strength and conditioning coach, or personal trainer. Athletic training is a very specific major but there are also other ways you can put it to use.