Wisdom teeth are your last molars, they come out usually around 17 to 21 years old. In some patients, they will not erupt, they'll be impacted, meaning they're stuck in your jaw, and some patients will not get wisdom teeth.
The reason for the removal of wisdom teeth is to prevent future gum disease. Sometimes you can get cyst formations which can cause damage to the adjacent teeth or the bones in your jaw. You can also get what is called pericoronitis, which is an inflammation of the gum. It is best to remove the wisdom teeth that are impacted for this reason, and sometimes when the wisdom teeth come out straight, you don't have to remove them.