A Simple extraction is one in which the dentist can remove the tooth simply by loosening the gums around it, grasping the crown above the gum line with a plier-like forceps and then moving it side to side until it loosens from the bone.  Teeth are normally held into the bone by a thin sheathe of  soft tissue that separates it from the bone like a sock separates a foot from a shoe.  This sheathe is called the periodontal ligament, and it is this structure which ultimately enables the dentist to remove the tooth.  The key to simple extractions is to rock the tooth side to side slowly enlarging the socket in the bone while at the same time breaking the ligament which binds the tooth in the socket.  

Complex (surgical) extractions

Unfortunately, not all extractions can be done by simply grasping the tooth with forceps and rocking it out.  What if there is nothing left above the gum line to grasp? Or what if the crown breaks off leaving the roots still in the bone? These things can and do happen, and any dentist that extracts teeth will have to deal with them routinely.  In these cases, it becomes necessary to surgically remove the tooth.    This is frequently accomplished by prying the root out using a sharp instrument that can be forced between the root and the bone surrounding it.  This technique is called "luxation".  In the case of multiple rooted teeth, the roots are first separated so they can be removed individually.  Unfortunately, not all roots or root fragments may be removed in this fashion. This means that the dentist must make an incision into the gums around the tooth and raise a flap of tissue exposing the tooth and its surrounding bone.  

Sometimes, after the flap is raised, there is enough tooth exposed to grab and remove it as in a simple extraction (#1 above).  Sometimes, the technique described above as luxation may successfully remove the tooth.  If luxation fails,  the dentist must take a handpiece (drill) and cut away some of the surrounding bone in order to gain a purchase on the tooth. After the tooth has been pried out of the artificially enlarged socket, the dentist then sutures (sews) the flap of tissue back in place so that healing can proceed normally.  

When a tooth does not fully erupt into the mouth, but remains below the gums, it is said to be impacted.  Impacted teeth can present special health problems for most patients, and they are generally removed to prevent future difficulties.  The extraction of such teeth proceeds like the surgical extraction explained above with a few modifications.  Sometimes, the only surgical procedure is the raising of the soft tissue flap. If after raising the flap, the extraction can proceed as a simple extraction, the tooth is said to be a "tissue impaction" because there was enough of the crown left above the bone to grab and extract with forceps.