Explain me half-sync/half-async pattern

I faced a mention of "half-sync/half-async" template in context of tuning performance of three tier application (front-end - backend-server - db):

One way to multi-thread a OLTP back-end database server is to create a thread pool based on the “half-sync/half-reactive” variant of the Half-Sync/Half-Async pattern.

I've read an article about "half-sync/half-async" pattern. The pattern was explained there via example:

//Represent synchronous layer
public class AsciiArtGenerator {  
    // Convert image to ASCII, long term operation
    public boolean convertToAscii(String imgPath, String outPath) {..}  
}  

// Represents an asynchronous layer, as it forwards client requests for further 
// processing and returns immediately. It receives results via notifications.    
public class NonBlockingDispatcher {  
    //Sends a request to the queue and returns instantly.  
    public void dispatch(final String imgPath, final String outPath) {..}  

    //Captures processing result and notifies the subscribed client  
    public void onResult(boolean result) {..}  
}

That use case appears very unconvincing to me.

Questions:

• Why just don't use AJAX / promises on client side (I suppose it's on JS)?!
• When do we need NonBlockingDispatcher at all?
• May you provide some more use cases from web development?