VPS Questions

I'm struggling to understand the concept behind a VPS.
If I were to purchase one, is it running a copy of my operating system elsewhere, giving me virtual access to it to install and run my own programs, thereby allowing me to turn my physical computer off overnights and still have that cloned PC running elsewhere?
Also, am I by living in Australia in any way restricted to certain VPS'?
Any suggestions on which VPS to purchase would be helpful, if and only if my thesis above is correct.

Thank you!