This is an infection around the crown of a tooth that is erupting, or trying to grow into the mouth.  It most often occurs in those age 17-21 in cases where the third molars (wisdom teeth) are coming into the mouth but do not fit all the way. Flabby gum tissue sitting next to, or over, the back of the half-erupted tooth can collect bacteria, food and debris underneath and an abscess/infection  can form.  The patient cannot open his or her mouth wide and the pain may travel down into the lymph nodes of the neck.  The lower wisdom teeth are effected much more frequently than the uppers.

A dentist will carefully lift the gum tissue behind the tooth and clean the area out.  Sometimes pus and blood will come out when the flap is lifted.  This can afford relief, but usually an antibiotic is used as well. (Amoxicillin 500 mg, or erythromycin in case of amoxicillin/penicillin allergy.) 
The sure and permanent cure is to have the tooth removed. This is usually (not always) done by oral surgeons, although your general dentist can relieve the pain temporarily. 
In some cases there is just a small flap of tissue over the wisdom tooth and all that is needed is a gum trim. More detailed information and drawings can be found at