What part of the eye secretes tears to keep it moist?

To understand this, you can simply divide the eye into three major parts: The eyeball, the eyelids and the orbit. To be able to function properly, the eyeball has to maintain moist. This is where the eyelids and the orbit take action. The orbit is the "hole" in which the eyeball is placed and the eyelids make sure the orbit is completely sealed so no infections and bacteria get inside the orbit. 

On the upper outer part of the orbit, there is an almond shaped gland, which is sort of a tear-producing factory. Trough small canals below the upper lid, these tears flow onto the eyes and keep them moist and clean. The distribution of the tears over the surface of the eye is facilitated by blinking. Then, the tears flow from the eyes  through canals into the lacrimal (tear) sac, from which they drain into the nose.