Wisdom teeth are the third (and final) set of molars that most people get and they do not make anyone any smarter. They usually come in while most people are in their late teens or early twenties and most dentists recommend that they are removed around the same time to prevent future complications.
If they grow in properly, then there is no problem and they can stay in your mouth. However, this is not usually the case and leaving them alone to grow in wrong can damage the surrounding teeth, jaw, and nerves.
The dentist will periodically take x-rays of your wisdom teeth to evaluate their alignment and make recommendations based on what he sees there. If your wisdom teeth are going to be harmful to the rest of your mouth, the dentist will recommend that they are removed. Removal is easier with younger patients because the roots have not yet fully developed and the bone is less dense. This makes the procedure simpler and recovery time much shorter.