Hand-eye coordination in 3D space
Short answer
Proprioceptic receptors provide a feedback mechanism from the body to the brain, telling the brain what our limbs are doing and where they are with respect to the body without visual feedback being needed.

Background
Muscles, skin and joints contain proprioceptic receptors. They sense position and movement of our limbs and trunk, they register force as well as heaviness. Examples of such receptors are limb tendon organs and possibly also muscle spindles, which contribute to the senses of force and heaviness. 

Proprioceptive sensations are influenced by visual input, but operate without it. The proprioceptive system is responsible for the ability to touch your nose with your eyes closed and the examples you have given related to catching a ball while not paying visual attention to the position of your hands.  

Afferent signals from these receptors are combined and processed in the brain. Together they form information about limb position and movement. This information is mapped relative to a central body map to determine the location of the limbs in space.  The proprioceptive senses, particularly of limb position and movement, deteriorate with age and are associated with an increased risk of falls in the elderly. 

Reference
Proske &amp; Gandevia, Phys Rev 2012; 92:1651-97