I have recently been educating myself about WCF and I have even written some production services using WCF. But I have never really looked too much into WCF until recently.
I am aware of the idea of the "proxy" design pattern. I am also aware of the use of a proxy with ASMX web services. But I am having a hard time understanding what a WCF proxy is and how it is used. I have looked thoroughly over the MSDN documentation about WCF, but I am still not grasping the big picture of the use of proxies with WCF services.
A proxy is an in-process representative of an out-of-process service. You call the proxy (which is easy), which setups up the communication channels etc. and talks to the remote service (which is hard).
See also http://msdn.microsoft.com/en-us/library/ms730144.aspx.