The pet glove is received from Kross. For details, see Farming Tools.
The pet glove is used to obtain monsters from all dungeons. These can do a large amount of all areas of farm work - they can water, weed, collect grass, harvest, destroy rocks, destroy wood, and gather fodder. They can also supply goods such as gems, milk, and wool. For details, see Harvester.
The pet glove is also used to enhance friendship levels. As friendship levels increase, the tasks performed will be more efficient (i.e. at four friend points, tasks will be performed better than at 1 friend point).
Pet glove is given to you by Kross. This event happens in the begginig of the game when you talk to him, after you have been to whale island.