What does it mean when a web service is asynchronous?

I know this is an old topic, but whether a web service is synchronous or asynchronous depends on the design of the web service and has nothing to do with Ajax. An asynchronous web service transaction proceeds like this:

1. The client calls the web service. In the call the client sends a callback end point implemented as a service by the client.
2. The web service returns a “message received” reply.
   …
   (Some other processing occurs)
   …
3. The web service completes its task, then calls the callback endpoint provided by the client.
4. The client callback replies with message received.

See Developing Asynchronous Web Services or How to: Create Asynchronous Web Service Methods