A-500S +DP-10 Half Damper Pedal

I have the Roland A-500S keyboard and the Roland DP-10 Half Damper Pedal in my home studio which I use mostly for synth and bass parts that come up (the keyboard, not the pedal). I am a guitarist and not a pianist but am slowly over the years teaching myself keyboards for fun and I had hoped to learn Garritan Orchestra in depth some extra long  and snowed in winter. Thus I have these questions because I don't know keyboard basics very well.
 
Here is my question. What is the "half damper function"? What does it do and does it even work with the A-500S?
 
I currently have a vocalist and pianist client who requested a sustain pedal on her project while she recorded piano parts. This was the 1st I had used it but I had it ready to go. The cable was patched to the HOLD jack on the side of the keyboard and I had the pedal set to "Half Damper Control" as prescribed in the sketchy Owner's Manual.
 
The client told me the pedal was not functioning. Initially, to troubleshoot, I then re-set the pedal to "Switch Control" and then she said it is working perfectly. The manual says to use this setting to have the pedal function like the DP-2 which is not a half-damper pedal.
 
So again my question, what is half damper (Google says this will let you finely control the decay of the sound and expressively recreate the complex characteristics of acoustic instruments e.g. piano and stringed instruments)? Does it work with the A-500S (which I was led to believe the entire series of keyboard were) and, if so, what does it do for piano as you depress and let up on the foot pedal?
 
Thank you kindly for any response.

Yes that video does explain the half damper function well, thanks!
 
I am unsure now whether the pedal was not working in half damper mode or the young pianist just couldn't recognize it; her Mother thought perhaps she was expecting only a traditional sustain pedal sound and thus would assume it wasn't working if it sounded differently.
 
Now that I know what the function really is, I can delve into it myself and test it out.
 
Many thanks!