Very often, there are teeth which are sensitive and painful  to sensations, due to recession of the gums from the tooth neck, which should normally be covered by the gingiva. In this case because of the pain as well as for aesthetic reasons, a surgical cover to the neck of the tooth is performed, taking a piece of gum from another in  donor place in the mouth or an artificial graft (which mimics the gingiva) and fixing it to the surrounding tissue.
Also, periodontal surgery covers surgical treatment of deep periodontal pockets, with a deep clean and removal of  inflammatory granulation which are inaccessible by conservative cleaning.