Skype is a half-duplex audio service, which means that only one person can talk at a time. Think of an old fashioned speaker phone or even a walkie talkie or Nextel. Most of the time, that's not a problem. However, there are some advanced uses of Skype in which the half-duplex clipping, or ducking, is a problem.
Here is an updated and simplified version of an article I wrote a couple of years ago on how to eliminate Skype Ducking. This version uses only Skype. The big "gotcha" with this configuration is that you must have excellent Internet bandwidth on both the caller's and the host's sides.