What is the idea of stop inheriting permission from parent site.

1. a publishing parent site which have 5 sub sites.
2. I wanted to define special permission on a sub site, so I access the sub site permission page and I stop inheriting the permission from parent site
3. Then I define three new groups at the sub site level.

But I am wondering about the following:-

1. Since I stop inheriting the permission from parent site and I define unique groups; why if I access the sub site permission I still can see the parent site security groups.
2. If I access a parent site group, from sub site and I remove all the users , then these changes will also apply to the parent site although I have chosen to stop the inheritance. And also if I modify the parent group from the parent site the effect will apply to the sub-site although the inheritance was removed ???

Best Regards