What's really the purpose of the Virtualizer?
I am unable to understand why you've asked this. Virtualizers make music cool. Using it, users can tweak music listening experience. It enables you to experience live concert in a car, for example.
The difference from 1% to 100% is also noticeable but it's not even close to the difference when the Virtualizer is disabled compared to when it's enabled.
Its because your speakers aren't that powerful. Just connect your device to a high-end speaker/headphone & feel the changes.
How does the Virtualizer work?
How does this sound effect simulate a live show music (atleast that's what it feels like to me)?
Demystify yourself when you are at a live concert. Your ear drums interface the air with special vibrations (sound waves) which gives you that feeling. At home, air hitting your ear drum doesn't have that specialty of live show. What virtualizer does is that it vibrates the air (hitting ear drum) in special way. In short, virtualizers just alter the sound in a special way.
How these algorithms work in background is out of scope of this site. To understand them, you need a strong background in Computer Science and Acoustics (Physics dealing with mechanical waves). Its thing of research. I can bet that even developers of PlayerPro haven't invested time & money to develop it. They have just used openly available libraries developed by research organizations, universities etc.