Here are the basic stages of a vacuum pumps operation with a general description of how it works using an example:
1. You have a 1m
3 container filled with a gas.
2. You expand that container to 2m
3.
3. The gas volume will increase with it so the gas occupies the entire space.
4. Once you've expanded it you divide it in half so you have two 1m
3 containers with half the gas in each.
5. You empty one container by reducing its volume to zero and forcing the gas out.
6. You remove the divider and allow the gas to expand to 2m
3 again.
7. You then repeat the process over and over, each time the amount of gas reduces.
That's all a vacuum pump does (but not as efficiently). It creates a low pressure area which allows the gas to expand into it (2 & 3), then 'cuts off' that gas from the rest (4) and then forces that gas out (5). It then repeats the process over and over (6 & 7).
For a better description and animations, see this site: http://www.absolute-vacuum.com/resources_whatisavacuumpump.php
This is another vane pump animation, demonstrating the principle I outline above:
http://www.mekanizmalar.com/vanepump.html