The part of these faucets that the output spout connects to have O-rings inside at the approximate locations shown by the red lines below. 

[![enter image description here][1]][1]

These O-rings seal the gap to the central post of the faucet around which the spout assembly rotates. Leaks can develop when:

1. An O-ring is torn for some reason.
2. Hard water deposits such as a calcium or lime deposit from evaporated hard water gets into the O-ring and breaks the seal.
3. The O-rings can get old and dry out so they become hard. Thus losing the rubbery compliance that is needed to create a seal.
4. Sometimes there is lubrication added to the zone where the O-rings reside making the rotating part move smoothly. If the lubrication loses its effectiveness it can cause the O-rings to wear and thus allow for a leak. 

You can check these O-rings by removing first the faucet handle and then the upper part of the center post assembly *(after first shutting off the supply valve at the wall under the sink)*. This should allow the spout assembly to be removed by pulling it up while at the same time rotating it back and forth some. Once removed the O-rings can be inspected. If they are hard, dry, torn or worn they will most likely need replacement. If it appears to be a loss of lubrication that can be restored by using a small amount of food grade petroleum jelly. 

**Note** you may find the O-rings reside within a slot inside the spout assembly or they may be in a groove that surrounds the upper and lower area of the center post portion of the faucet.

Typical Moen Kitchen Faucet exploded parts assembly:

[![enter image description here][2]][2] 
 


  [1]: https://i.sstatic.net/OubRj.jpg
  [2]: https://i.sstatic.net/1wh0v.png