Although there are many aspects of this law, the most important is the aspect that has to do with the "portability" of health care. The law was created and enacted in an attempt to deal with that issue.
For most Americans, health insurance comes with the job. We are typically insured by plans that we qualify for when we get hired at a given job. If we leave that job, we typically stop being eligible for that health insurance plan. The HIPAA was created in an attempt to deal with this problem. If your health insurance is tied to your job, it becomes much harder to leave that job in hopes of finding something better. In addition, if you lose your job (due to being laid off or the like), you lose your health insurance until you find a new job. This can be a very stressful situation.
In order to try to prevent problems like this from occurring, the HIPAA was created and enacted in 1996.