Gomukhi is a special cloth cover made for a lala to do mantra chanting. According to the Shastras, you have to cover your mala (rosary) when you are doing mantra chanting. You are not suppose to use your index and little finger.
The word gomukhi means 'in the shape of a cow's mouth'. It is a small bag which resembles the shape of a cow's mouth. The mala and your right hand are both placed inside the gomukhi so that they are obscured from view. With your hand in the bag, you then begin to rotate the mala, the bottom of which is supported by the bottom of the bag.
A gomukhi is very light, doesn't interfere with the practice of japa and prevents other people interfering or becoming curious about your practice. It can be used when you walk along a street or when you leave your house.